You can still be the favourite, but during the ending recap it can change your future from Empress to "courtesan", since you can't officially be the Emperor's wife.
Viewing post in Caliross, The Shapeshifter's Legacy comments
You can only see the ending once in the game. Technically you could say it's not set in stone, but unless you use the debug tool, you aren't going to watch the ending sequence again afterward.
I'd have to double check, but I think you get a variation of the courtesan ending if you are the favourite while being involved with Eliza.
Did you check the walkthrough?
https://docs.google.com/document/d/16XOUX_KXz800cLQ7VledpazkEZjviWRPpXzR3iswfmE/...
Reading your comment I even decided to update the entry for the first puzzle in the first temple, hopefully the solution is clear enough to follow.