Any character with simulacrum, or better yet, wish.
At 20th level, you are a paragon among mortal creatures, being able to contend with fierce monsters on your own, and some of the most powerful enemies when in a group.
As such, a simulacrum (which is just a slightly weaker version of yourself) is the ideal companion to send with your party if your are sanctum-bound:
You shape an illusory duplicate of one beast or humanoid that is within range for the entire Casting time of the spell… the illusion uses all the statistics of the creature it duplicates.
This simulacrum lets you loan most of the abilities that you would contribute if you were physically present with two exceptions:
it has half the creature’s hit point
The simulacrum lacks the ability to learn or become more powerful, so it never increases its level or other abilities, nor can it regain expended spell slots.
Its inability to use spell slots is the most crippling, but you can get around this by using wish to create a new simulacrum each day:
The basic use of (wish) is to duplicate any other spell of 8th level or lower.
…and then having the simulacrum cast teleport to return to your party. This will dismiss the former, now spent simulacrum and provide your party with a brand new illusion of yourself with fresh spell slots (minus a 9th-level and 7th level one).
You will also need to have your simulacrum cast plane shift and then teleport if the party is on another plane of existence. This would cost the simulacrum’s 8th level slot as well. You could avoid expending the simulacrum’s 7th and 8th level slot if the character is willing to ferry the simulacrum to the party which would take less than a minute outside of the sanctum.
So which classes get access to these spells?
Simulacrum is a wizard spell, so you would need to be a wizard or a bard who can gain it through the Magical Secrets class feature:
By 10th level, you have plundered magical knowledge from a wide spectrum of disciplines. Choose two spells from any classes, including this one. A spell you choose must be of a level you can cast, as shown on the Bard table, or a cantrip.
You learn two additional spells from any classes at 14th level and again at 18th level.
Wish and teleport are available to sorcerers and wizards (and bards once again using Magical Secrets for wish). A cleric of the Arcane Domain could also gain one or both of these spells through the Arcane Mastery class feature:
At 17th level, you choose four spells from the wizard spell list, one from each of the following levels: 6th, 7th, 8th, and 9th. You add them to your list of domain spells. Like your other domain spells, they are always prepared and count as cleric spells for you.
In summary, these classes:
- Cleric (Arcana Domain)
note: Sorcerer doesn’t get easy access to plane shift if that is necessary, and have no summoning spells which is mentioned later in this answer
note 2: Wizards have the most diverse access to summoning spells, so are likely the best choice, but clerics and bards still get enough to where they are not completely outshined
First, you want enough magic items to gear up your simulacrum. Preferably including a handful of staves or similar items that can regain charges if you aren’t using the wish and teleport option for when the simulacrum runs out of spell slots. If you are worried about the half-health, you could also send the simulacrum with an amulet of health to bolster its survivability.
Secondly, if on the same plane of existence, you can also help from your sanctum by using a crystal ball which affords unlimited scrying:
The typical crystal ball, a very rare item, is about 6 inches in diameter. While touching it, you can cast the scrying spell (save DC 17) with it.
Not only would this let a wished simulacrum see the location they are teleporting to (to avoid a mishap), you can also provide key intel to your party (either through sending for either class option except sorcerer, or by using a special variant of the crystal ball, see below).
If you have access to legendary magic items, each crystal ball variant could be extremely useful. One would let you attempt to read the minds of enemies you are scrying on, one would let you communicate with the party telepathically, and the other would provide truesight for your sensor.
Next, if you are using wish for fresh simulacra each day, get yourself a helm of teleportation. This way you can save your simulacrum from having to use their 7th level spell slot to get to the party. Make sure to tell the expended simulacrum to bring the helm back at the end of the day. Some days you won’t be able to do this, as you have to wait for the helm to regain slots (since it only regains 1d3 per dawn), but the extra power behind that 7th level slot is nothing to scoff at.
Unfortunately, no summons other than found familiars and created homunculi (for wizards) and steeds (for bards with Magical Secrets) last more than an hour. To send more powerful summons, you will need to cast planar binding to extend the duration of the summoning spells. With this, the only real limitation is the cost since each casting of planar binding costs 1000 gp. Your best summons with this technique are:
- conjure celestial for clerics to summon a couatl
- conjure elemental for wizards to summon any of these elementals
- infernal calling for wizards to summon any of these devils
- summon greater demon for wizards to summon any of these demons
Bards can learn any one of these spells, or conjure fey, through Magical Secrets (assuming they used their other options for wish, teleport, and plane shift), but sorcerers don’t get access to any of them.
It is worth noting that any demon summoned will not be dismissed immediately after 24 hours but instead turn hostile for a few rounds. However, your party should be able to deal with them as they aren’t particularly high CR.
It is highly beneficial to cast planar binding at 9th level. Not only does this let you exert control over more summons, it saves money on any individual summon (since each planar binding costs 1000 gp). With time to prepare you could get your ideal set of summons bound for a year. Just send them with your simulacrum and the party gets a large power bump.
If you are using the wish and teleport strategy, your simulacrum could even bring 8 chosen summons per day.
Another good, yet costly, idea is to create new summons each day that are customized to the specific challenges that the party is facing. You could add to your team of summons using 7th or 8th level spell slots (since wish is taking up your 9th level slot) at the cost of 1000 gp per summon.