I know that music from the baroque era was composed with the assumption that performers would add their own embellishments (when viable, not for canons or fugues). I've also heard that Mozart didn't write out all details, but assumed that the performer would realize the music on his own.
I have two questions regarding this: For which music should I not do this? Does this practice end at Beethoven's era? I've heard that it was over by Wagner's time. I just want to know which music is considered incomplete without further creativity by the performer(s), and which is not.
My second question is: Do all roles get to do this, or only continuo? Because if all roles get to add stuff, then I, as a harpsichordist, have to be much more careful with what I add in addition to the written notes. If, however, I know exactly what every one else will be playing, then I can more confidently come up with my own parts, knowing that they will work harmonically and contrapuntally with the rest of the music. If every role got to add, then I'd personally only do it to chord based music, while sticking to chord tones. If only I got to add, then I'd do it to any music in a way that maintains counterpoint, and which doesn't add dissonance.
Edit: Naturally, I will add what I think sounds good, or add naught at all if that's what I prefer. I am not asking for artistic guidance. What I wonder about is the intention of the composer. During which time period was the written score considered the complete and final music? When did the norm of realizing the music in one's own way end?