First off: Luma doesn't have less HP, it actually has more on 1v1 to cope out with the 1v1 multiplier.
Second off: The largest part of her moveset, especially without Luma, is unsafe both on shield and on whiff, and that is despite shields being what they are in this game, Nair being one of the few exception, instead having the problem of having swiss cheese hitboxes.
Third off: the only stat she has high is her air acceleration, the sixth best in the game. Everything else is either average or barely above average, except her fall speed
About Luma's movement, it's pretty simple: There is a zone that Luma always aims to be in when tethered and another one when dethered, I'll label this "anchor zone". Pre-patch when he was tethered, that zone would attract him like a black hole and constantly push back his position, most notably with Bair and DTilt. However, since Luma can't move, jump, shield, dodge, land and grab, but only has filler animation for that, he won't actually do any of those, and that means that if he throws an attack, he won't be able to change his anchor zone until he is done not with his FAF, but the whole animation lenght.
That's why Jab used to be what it was, to safely move him around. Without that, if he attacks he has to either wait the entire animation out or commit to another attack, DA out of all, to get out of the way, which just makes him a sitting duck when coupled with the worse hitboxes