A Necromancer of the Creed of Tomes is balanced, any other is over-powered.
Base Class: Balanced
The base class is very similar to a Bard: it has the same number of Spells known, for example.
It has only one more Cantrip, at the cost of a lower hit die (d6).
Its Vitality Shift is interesting. The fact that it can transfer up to 400 Hit Points at level 20 may be scary, but on its own this feature is not a problem due to the limited number of uses per day -- up to 5 -- and the fact that it is a transfer: any Hit Point taken from another must still be healed, in the end.
There are a few potential for abuses. A horde of followers is the obvious one, but the DM should be able to curtail that quickly.
Eternal Youth is on the powerful side. Few classes gain Proficiency in a second major Saving Throw. If the character also takes the Resilient feat for Dexterity, this leads them to covering all 3 major ones, and therefore being a bit of a pain to deal with. It comes online at level 18, though, when the character already has access to 9th level spells...
Creed of the Departed: Overpowered
The Undead Minion feature is hard to judge, due to its open ended nature, although there are good limits in place:
- The Necromancer must expand its Hit Dice to create and maintain a creature.
- The number of Hit Points of the creature is rather limited: 40 + 1d6 at level 20.
- The abilities of the creatures are trimmed down, with penalties and restrictions.
Even the Conduit Walker feature is clearly copied from the Find Familiar Spell: same range, same use of Reaction.
The Sheperd's Resolve lifts the speed penalty, and adds another 1d6 of Hit Points to the Undead Minion. Both are minor gains.
The Animator Style is concerning, or at least 2 out of 3 options are:
- Adept Awakener seems mild enough, just a few bonuses here and there.
- Giant Rouser causes some concerns. Raising a Huge creature seems likely to open up some shenanigans, and the extra +5 to the CR of creatures one can raise doesn't help.
- Undead Magnate also causes some concerns, in the Action Economy sense. The ability to have up to 6 creatures under the player's control is much more potent than having 1 creature with 2 attacks, and the reduction in Hit Points doesn't make up for it.
Still Life is a ribbon; little enough mechanical effect.
And Legendary Animator causes concern again, building upon Animator Style: 6 Huge Creatures will cause a lot of mayhem...
Creed of the Siphon: Overpowered
Sycophant is problematic. There is no other feature in the game which does not place a limit on the amount of Hit Points one can heal. For example, the Champion's capstone ability only heals them up to 50% of their Hit Points. Also, in combination with Vitality Shift it allows regenerating a significant portion of the party Hit Point pool.
Learned Siphoner is also problematic. First of all Necrotic is not as oft resisted as non-magical damage, or even Fire and Cold, so the ability to have a Fireball deal Necrotic damage is problematic in and out of itself. Worse, though, is that it compounds with Sycophant: 1/3 of the newly dealt damage heals the Necromancer after all...
The sub-features of Learned Siphoner are mixed:
- Essence Weaver is overpowered: the extra damage doesn't matter, the problem is the healing. A limit of Sycophant + Vitality Shift is the number of uses of Vitality Shift: Essence Weaver does away with this limit, giving the entire party infinite health.
- Vigor Thief is alright: once per Long Rest, so it's fine if it's a bit powerful.
Ascetic Dominion offers cheap resurrection. By level 10 some forms of resurrection are available already, and the level of exhaustion suffered prevents really jumping back into the fray. I could foresee mass-resurrection abuse: resurrecting an entire village, 1 Hit Point per villager. Whether that can really be exploited is less clear, however.
Everlasting is one of many abilities to thwart death available to players; once per Long Rest is definitely fine.
Blood Funnel is concerning due to its ability to steal Hit Points from foes; but given Sycophant it doesn't add much...
Note: I couldn't see all the text for Blood Funnel, due to formatting issues and apparently a "cut" copy/paste; I may have missed something.
Creed of Tomes: Balanced
Initiate of the Tome is fine. The Refined Spell is the only powerful feature, and it's a once per Long Rest one.
Arcane Shift is once again a transfer, so none too problematic, especially given the 1 Spell Slot per shift combined with the limited number of possible shifts.
Evercasting is a good capstone. It should not kick in too often, due to the (cumulated) CR 10 requirement, and its limitation to lower-level Spell Slots limits abuse: Action Economy dictates that again powerful foes, the higher-level Spell Slots will be the most necessary.
The Augur's Acumen really depends on the Acumen. Of interest, there is no possibility to switch a known Acumen for another, hence it is not possible to end up with all high-level Acumen and no low-level one.
I noted 2 interesting Acumen, which I think could be accidentally construed as more powerful than they are:
- Channeler: This is essentially Blindsight to 10 ft. The limited range limits its power, fortunately.
- Gale Rider: Abilities to ignore difficult terrain and walk across water (or lava) are rare, and spells have limited uses. The character has access to 7th level spells at this level, though, so can use Fly and similar for the occasional obstacle.
Overall, I find Augur's Acumen fairly balanced.