It varies for my characters what I will do

My LS SW started as blindly loyal to the empire and the emperor specifically. He rooted out the corrupt elements of the empire and pushed reform where he could but believed the emperor had a plan and the good of the galaxy in mind even if he couldn't see it. Then yavin and ziost happened and broke him. I think he spent the time between the end of SoR and the beginning of KOTFE stuck between disillusioned bitterness for the empire (helped by the reveal of zakuul and valkorians own comments as a ghost) and deep regret for the role he played as the emperor's top lackey. By iokath he was no longer sith but definitely not Jedi, the only code he follows is his own. He's turned his back on the empire to secretly help the republic, but I can't see him on either faction so he stays with the alliance.

On the other hand my neutral Inquisitor is pleasantly surprised by acinas reforms and the direction the empire is going, he craves power but after his time leading the alliance isn't really interested in ruling any longer. He'd be content to serve in the new dark council and keep his political skills sharp while looking for more and more ways to amplify his strength in the force and find the key to immortality that doesn't require eating a planet and turning the world against him. He'd rejoin the empire if allowed.