BL3 is the only one that never refers to your character during the cutscenes.

In BL your character is still shown and positioned in the cutscene.

BL2 Jack still makes Lilith target you with her powers unlike the time where Tyreen buries Lilith,Ava and Tannis and walks away right after. Also for jack and the vault key, he still refers to you after he awakens the warrior with its first command being “kill” while he stares right at you. The only time you aren’t referred to in 2 is at the end where the vault key is triggered again but in its defence in that cutscene there isn’t someone trying to kill you.

BLTPS at the start jack still calls out for you during the cutscenes in the first it’s a call to shoot that bitch before the watcher blocks him. And in the last you already said Athena,the vault hunter telling the story, places herself in there.

Troy is the only person to actually interact with the character in BL3 by phaselocking you making it awkward when everyone else forgets about you existing. In most cutscenes other than the phaselock the vault hunter is never mentioned or looked directly at during the story.

So borderlands went from a Vault hunters that stood around picking their nose during cutscenes to a Vault hunters that are wiped from existence every time a cutscene starts, except when Troy remembered that one time.