In earlier editions of D&D, multiclassing between spellcasters was generally pretty terrible. Spell levels increased in power super-linearly, so losing access to high-level spells was much worse than gaining double the number of low-level spells.
5e made this substantially better - you add together your levels to determine the spell slots you have, so a Wizard10/Cleric10 still gets 9th level spell slots just like a Wizard20; the drawback is that neither class gives you spells known above what each class at level 10 caster can know (5th level spells) - a lot of spells scale up in power if you use them in higher-level slots, so that 9th-level slot is still useful for a big attack, but it's not the equal of an actual 9th-level spell.
However, 5e also introduced a totally different spellcasting mechanic - Pact Magic - and then utterly failed to address multiclassing with it. A Warlock10/Wizard10 just... has 5th level slots. Two more than a Wiz10 would normally have, and those extra two refresh on a short rest, but still, this sucks.
There's not even an effective, natural way to multiclass two Pact Magic-using classes together. The Warlock is the only such class in Core Rules, but it's a popular spellcasting mechanic and shows up in homebrew material.
Related to this, the Spellcasting multiclass rules also cover "half-casters" (like the Paladin or Ranger) and "third-casters" (like the Eldritch Knight or Arcane Trickster) - they add 1/2 or 1/3 their levels to a full-casting class's levels to figure out spell slots. But again, Pact Magic has no obvious way to do "half-casters", which severely limits how homebrew can approach Warlock-ish stuff.
But Here's The Thing
The special thing about Pact Magic is that your spell slots regen on short rest, so you don't need too many of them. But you know who else kinda has spellcasting that regens on short rest? MONKS. There are actually tons of parallels here.
One, Monks have a ki pool equal to their level. Spellcasting monk subclasses vary on how much ki they charge, but the consensus among homebrewers seems to be that the decent subclasses all charge ki = spell level (sorry, Elemental monk, you're suboptimal) (Sun Soul charges level+1 for their Burning Hands, but casts it as a bonus action, so worth the cost). If we convert the Warlock's spell slots into "spell points" at that same rate, they have a pool of points roughly equal to their level, too. (It jumps around a bit as their spell slots are "chunkier", but it's always roughly at that rate.)
Two, spellcasting monks get access to a maximum of 5th level spells, like a half-caster, and get access to them at approximately the same levels as half-casters do. They can spend extra ki to power up their spells, too, same as spellcasters can use higher-level slots.
The Warlock caps out at 5th level spell slots, but gains them at the rate of a full-caster. Then, when a full caster would get access to level 6+ spells, the Warlock instead gets Mystic Arcanum, letting them learn and cast some higher-level spells too.
All in all, it really feels like there's a consistent pattern lurking under the surface here, waiting to be expressed by just slightly tweaking the classes. I call this: the Mana-usage feature.
So How's This Actually Work?
Here's the plain details of mana-usage:
Warlocks get a mana pool equal to their level (replacing their spell slots). It refills on short rest. They can cast a spell that they know by spending mana equal to its level (and can spend additional points to cast it at a higher level).
At 1st level Warlocks can only spend 1 mana on a given spell. This increases to 2 at 3rd, 3 at 5th, 4 at 7th, and 5 at 9th. This also determines what level of spells they're allowed to learn, in the same fashion as other full casters.
At 11th level they get their first Overcharge: usable 1/long rest, this lets them cast a spell for free, as if they had spent 6 mana on it. At 13th level they gain an additional overcharge, worth a free 7-point cast; at 15th, another overcharge worth 8; and at 17th, a final overcharge worth 9. (So, by the end they have four Overcharges, each usable 1/long rest: a 6-point, 7-point, 8-point, and 9-point.) Alternately, instead of getting a free cast, they can spend an overcharge to refill their mana pool by 2 fewer points (the 6-point overcharge can be spent to refill 4 points of mana, 7-point overcharge can refill 5 points of mana, etc).
As a class feature, warlocks still learn one 6th-level spell at 11th level, 7th-level spell at 13th level, etc. These spells cannot be swapped out like their other spells known, which continue to be limited to a max of 5th level.
For Monks, just rename their "ki pool" to "mana pool", etc. They are otherwise unchanged. (Secret bonus: the name change pulls Monks slightly away from the unfortunate Orientalist-fetish vibes it's always given off. You're just a slightly magical fighter class, cool!)
Warlocks are "full" mana-users; Monks are "half" mana-users.
Your mana pool is equal to the sum of all your levels of mana-using classes. Whether they are "full" or "half" doesn't matter; a Warlock10/Monk10 has 20 mana in their pool.
To determine maximum mana usage and overcharges, add together all your "full" mana-using levels, and half your "half" mana-using levels, then consult the table below. So, for example, a Warlock10/Monk10 uses the "15" row in the table.
|1||1 mana/spell max|
|2||1 mana/spell max|
|3||2 mana/spell max|
|4||2 mana/spell max|
|5||3 mana/spell max|
|6||3 mana/spell max|
|7||4 mana/spell max|
|8||4 mana/spell max|
|9||5 mana/spell max|
|10||5 mana/spell max|
|11||5 mana/spell max, 6mana overcharge|
|12||5 mana/spell max, 6mana overcharge|
|13||5 mana/spell max, 6mana + 7mana overcharges|
|14||5 mana/spell max, 6mana + 7mana overcharges|
|15||5 mana/spell max, 6mana + 7mana + 8mana overcharges|
|16||5 mana/spell max, 6mana + 7mana + 8mana overcharges|
|17||5 mana/spell max, 6mana + 7mana + 8mana + 9mana overcharges|
|18||5 mana/spell max, 6mana + 7mana + 8mana + 9mana overcharges|
|19||5 mana/spell max, 6mana + 7mana + 8mana + 9mana overcharges|
|20||5 mana/spell max, 6mana + 7mana + 8mana + 9mana overcharges
"Casting" Monk subclasses, like Way of the Elements, can use overcharges earned from multiclassing in a full-mana-user like normal; they can cast their known spells at a higher level, or recharge their mana pool. They do not learn any higher-level spells, however. Non-casting subclasses, like Way of the Open Hand, have no scaling-mana abilities, and so can only use overcharges to recharge their mana pool.
There are no "⅓ mana-user" classes (like Eldritch Knight or Arcane Trickster) yet, but they do effectively exist due to the multiclassing rules in the next section (and are a good target for homebrew). ⅓-users add ⅓ their level to other mana-using classes to find their effective Mana-User Level, and add half their level to their mana pool (rather than their full level like ½-users do).
Interactions with Normal Spellcasters
The above rules give us a unified framework for handling multiple "recharges spells after short rest" casting classes. However, they don't help with multiclassing mana-users and spell-casters together, which are still extremely suboptimal.
After some thought, I believe a simple and workable solution is to treat your spellcaster level as a ⅓ mana-user class, and vice versa. That is, a Warlock10/Wizard10 would spellcast as a 13th level Wizard (having 7th level slots, but only knowing up to 5th level spells from their Wizard levels) and mana-use as a 13th-level Warlock (having a mana pool of 15, spending up to 5 mana/spell, and having both their 6 and 7 mana overcharges, but also knowing only up to 5th level spells from their Warlock levels).
Second, mana and spell slots can be spent interchangeably. If you know a spell from a spellcasting class, you can cast it by spending mana equal to the level of slot you would otherwise use (subject to your normal mana spending limits) or by expending an appropriate overcharge to cast a spell at 6th-level or higher; similarly, if you know a spell from a mana-using class, you can expend a spell slot of the appropriate level to cast it instead.
If a class ability would let you use a spell slot for any non-casting purpose (such as Paladin's Smite, or Sorcerer's metamagic pool recharging), you can spend mana equal to the desired slot's level (again, subject to your mana spending limits, or spending an appropriate overcharge for higher-level slots); similarly, if you have an ability that costs mana, you can instead expend a spell slot of a level equal to or higher than the mana cost.
Interactions That I Think Are Fine
Mana-locks mostly function like normal Warlocks, but their interactions with two other spellcasting classes do change a little.
The Paladin/Warlock combo relies on quickly-recharging warlock slots to power more frequent Smites. The only change in using Mana-lock is that the Paladin can do more lower-level smites; a Pal3/War17, for example, would have 18 mana, potentially powering 18 +2d8 smites per short rest, versus the RAW-lock which gets 4 +5d8 smites per short rest. The Mana-lock can also burn all their overcharges to recharge an extra 22 mana per long rest, for more smites, while the RAW-lock is limited to using their Mystic Arcanum for their original spellcasting purpose.
So, theoretically this just means that a Paladin could be adding +2d8 to nearly every attack over a short rest. That's useful, sure, but it means they're not opening combat with a powerful +5d8 smite and likely taking an enemy out right away. The raw numbers look bigger, but you really have to take the action economy into account when evaluating this sort of thing. The weaker, more frequent smites probably roughly balance out with the smaller number of more powerful smites that the RAW-lock is restricted to.
(That said, the Mana-lock still can open combat with a big smite, then use small smites later in combat, which is probably a best-of-both-worlds thing. Impact unclear; it's probably still usually better from an action-economy perspective to do larger smites less frequently.)
The other interaction is with Sorcerer; a Warlock/Sorcerer multiclass (the "Coffee-lock") can start their adventuring day spending several hours repeatedly unweaving their Warlock slots into metamagic points, weaving them into Sorcerer slots, then short-resting, finally starting their adventure with a ton more Sorcerer slots for the day. This interaction is mostly just a degenerate rules-abuse that isn't worth explicitly disallowing in rules, in favor of just house-banning such nonsense (short rests weren't meant to be abused like that). That said, the Mana-lock doesn't actually make it any more powerful. A 10/10 mix can produce 15 metamagic points out of mana every short rest, producing a pair of 5th level slots; a RAW-lock can only produce 10 (for a 5th and 2nd slot), but ➀ the 10/10 split is suboptimal, a War11/Sorc9 can produce 15 points per short rest, and ➁ Pact Magic/Spellcasting multiclassing is absolute shit in the RAW rules; if you use the "each counts ⅓ to the other" multiclassing rules I list up above with RAW-lock, you immediately get the 15 points per short rest even with a 10/10 split. (And I recommend doing so; the ⅓ rule actually works really well overall.)
So overall, the multiclass interactions seem to be well-handled and nice.