Autistic DM (he/him)
Spell list looks good to me.
The same thing as Divine Warrior that Paladins take (from Tasha's) and the Druidic Warrior that Rangers can take (from Tasha's). Arcane Warrior very specifically allows you to learn two cantrips from the Wizard spell list, have them count as Arcknight spells for you, and be able to swap out one of them with another Wizard cantrip on a level up.What does this fighting style do ?
The rest of their Fighting Style options are Defense, Dueling, Two-Weapon Fighting, Great Weapon Fighting, Thrown Weapon Fighting, Interception, and Blind Fighting.
Then, at level 10, I give them an additional benefit (called your "Arcane Fighting Style") based on what fighting style they chose at level 2, which merges arcane magic with their fighting style. For example, Arcane Warrior lets you replace an attack from the Attack action with a cantrip, Blind Fighting gives you a 10 foot range of seeing into the Ethereal Plane, Thrown Weapon Fighting lets you summon back your thrown weapon after you throw it, Great Weapon Fighting lets you reroll 1s and 2s from your Spell Strike damage dice once (I'm considering putting a limiter on the amount of dice you can reroll from the Spell Strike damage, though). It was just a cool idea that I had been brainstorming, making an Arcane Gish class be able to merge spell and sword in unique and awesome ways.