Shadow Blade, Overchannel and Sneak Attack Dice

If a level 14 Evocation Wizard with 3 levels in Rogue, uses their Overchannel ability on a 5th level Shadow Blade spell and lands an attack against a creature dealing 4d8+Dexterity modifier + 2d6 sneak attack damage.

Because the Sneak Attack counts as “extra damage” (taking on all the damage properties that the Shadow Blade possesses) is it also maximized by Overchannel?

Does Overchannel even work on the Shadow Blade’s damage in the first place?

My first impression is yes to both of these but I might be overlooking something.

How does an Evocation Wizard’s Overchannel ability interact with Chaos Bolt?

With the release of Guildmaster’s Guide to Ravnica, characters were given new background options. Some of these options add spells to a character’s spellcasting classes. One of these is the Izzet Engineer, which allows for any spellcaster to learn and cast chaos bolt, among other spells.

Izzet Engineer relevant snippet:

Spell List
For you, the spells on the Izzet Guild Spells table are added to the spell list of your spellcasting class. (If you are a multiclass character with multiple spell lists, these spells are added to all of them.)
Spell Level: Spells
Cantrip: produce flame, shocking grasp
1st: chaos bolt, create or destroy water, unseen servant

Chaos bolt follows:

You hurl an undulating, warbling mass of chaotic energy at one creature in range. Make a ranged spell attack against the target. On a hit, the target takes 2d8 + 1d6 damage. Choose one of the d8s. The number rolled on that die determines the attackā€™s damage type, as shown below.

d8 Damage Type
1 Acid
2 Cold
3 Fire
4 Force
5 Lightning
6 Poison
7 Psychic
8 Thunder

If you roll the same number on both d8s, the chaotic energy leaps from the target to a different creature of your choice within 30 feet of it. Make a new attack roll against the new target, and make a new damage roll, which could cause the chaotic energy to leap again.

A creature can be targeted only once by each casting of this spell.

At Higher Levels. When you cast this spell using a spell slot of 2nd level or higher, each target takes 1d6 extra damage of the type rolled for each slot level above 1st.

Combine this spell with the Wizard Evocation tradition ability of Overchannel:

Overchannel
Starting at 14th level, you can increase the power of your simpler spells. When you cast a wizard spell of 1st through 5th level that deals damage, you can deal maximum damage with that spell.

I found another question referencing wish-ing to chaos bolt. The answer references the fact that chaos bolt is not a Wizard spell, and therefore the asker’s desired outcome does not work. However, a key point of text from the Izzet Engineer (emphasis mine):

For you, the spells… are added to the spell list of your spellcasting class.

This means it is now possible for a 14th-level Izzet Engineer Evocation Wizard to choose to maximize the damage of a casting of chaos bolt.

What happens?

Does the spell continually leap to new targets until the caster chooses no target? Since the damage is maximized, is it dealing Thunder damage each time?

Am I simply too excited about this possibility? Should the 2d8 should be rolled as normal to determine damage type and leap potential, but then the spell deals 22 damage (8+8+6) regardless of the roll result?

Can someone with vulnerability to necrotic damage benefit from resistance, in regards to the Evocation wizard’s Overchannel feature?

Overchannel (Evocation Wizard feature) states that the necrotic damage it deals ignores immunities or resistances to its damage – but something like vulnerabilities would still be applied.

If I am vulnerable to necrotic damage, then gain resistance to necrotic damage, do I:

  • Receive normal damage from Overchannel as the two void each other?
  • Ignore my resistance and deal double damage from being vulnerable?