What if you would bring companions back in fully voice acted sidequests dedicated to them?

Example:

Jaesa Willsaam

Default (non sith warrior classes)

Dialog with npc defines Jaesa's alignment.

Dark: We are chasing dangerous artifact

You find out that dark jedi is also looking for dangerous artifact and there was another sith lord looking for same artifact, but dark jedi killed him/her.

Light: We heard we could find potential jedi ally here

You find out that this jedi is chasing sith lord that is trying to find dangerous artifact.

With sith warrior Jaesa comes to you instead npc and together you chase sith lord (light) or artifact (dark).

How about making companions part of main story same way than in class stories?

I know, I know, there too many companions now to include all of them, so:

New chapter, you can choose from 2 or 3 companions, companion 1, companion 2 or companion 3, if you killed companion 3 you can choose companion 4 instead or vice versa.

Companion 1: Dialog in story, companion comments about something and MC responds, dialog countinues.

Companion 2: Dialog in story, companion comments something different and MC responds something different, dialog countinues same way than in example above.

Deepening relationship/making them feel that they are part of alliance instead just absent:

Why companions are not seen in main story, like they don't seem to exist anymore?

Because they are doing some other super important alliance stuff, in sidequest you help them and deepen bond with LI if you did not kill him/her.