I think it has to do with the ambition for sure. I tried to go for a peaceful end for Revaire while romancing Clarmont as a Arland princess and had to reset multiple times because I couldn't get Sarya to confess to me either, which ended up with Clarmont dying and my poor princess widowed before marriage (and also a bad end). I ended up resetting multiple times trying different things, and Sara's respect and friendship seems to be tied to rebel approval. I ended up having to redo my character build to make sure I had at least 250 persuasion to get Katyia's legacy as a choice by the time the speech comes around. I noticed that once I did, I received Mrs. White's gift during week 3, which I didn't despite having the rebel approval bar at 3.5 before restarting. I think you also need to find all rebel secrets and find out who the true murder is too during the trial and complete a successful complete defense.
Incidentally, I managed to get perfect completion of the play and noticed that it greatly boosted approval all around in general. It is definitely not easy (I had to do a lot of planning to make sure I had the minimum stats based on some guides), but if you play around with your stats to make sure you have at least 250 persuasion, it should be a lot easier. I chose to play a lead role in the play and got roped into playing Serah. When I tried to pick another role, Jaslen forced me into Serah's anyways. I don't know if things will be different if you chose to work backstage. Hope all of these observations help you get Sarya to open up to you!