i screwed around with it and have no idea how the fuck homing actually works
It's one of those things where the base rules are relatively simple but the various interactions can create a really involved system.
-Homing always moves toward your opponent, but you have some directional influence over your exact trajectory.
-You can't do any other movement until the homing ends (and it only ends by getting point blank with your opponent or with an attack), but you can do any air normal/special/super, and you can also block.
-If you tap the homing button while already in that motion, you get a temporary burst of speed.
-Most attacks done while homing conserve momentum.
The last two points are where a lot of the movement tricks in the game come from, and also what allow people to cover so much space so quickly without needing absolutely insane reflexes to actually be a threat.
Why would you call it a traditional fighter?
To make it clear that it's still closer mechanically to games like Guilty Gear or Melty Blood than something like Smash Bros. or Senko no Ronde. It still had chains, traditional dashes (and air dashes), projectile rules are similar to other 2D fighters, the overall game flow is similar to other anime fighters (even if neutral takes place in 50x the screen space). At a first glance, that's not entirely apparent, especially with all of the flying around (I couldn't blame someone for thinking the game was Psychic Force: Waifu Edition if they saw the game blind).
like most fighters, AH3 desperately needed a better tutorial
There is a tutorial manga for the game. Just... uh... don't go look up that author's other works with other people around. (That link itself is completely safe for work... well, as safe as AH can be, anyway.)