My wife and I have watched Bridgerton a few times; it's quite a silly soap opera confection with all sorts of historical inaccuracies! But amusing. The actor playing Francesca is clearly not playing the piano for the soundtrack. The sound of the instrument is also wrong, as it sounds like a modern instrument, and the instrument pictured is supposed to look like it's from the early 19th century. The string players in the quartet or other musicians pictured are also not playing music for the soundtrack itself. They may or may not actually be musicians. I've often wondered if the actors don't have to speak, why not use real musicians? I think it has to do with the way they film sequences within a scene, the choreography, the sound recording and editing, etc.
Easier to add it later, I guess.