I forgot to add that there is a thread of Android 13 problems, but I’ve opted to stick with A11 due to the fingerprint sensor debacle. As a result I haven’t been following that thread. Maybe someone else can link you to it.
Edit:
I happened to find the thread FP3+: Issues with Android 13 update it has over 300 posts so it way take a while to digest. Note that there has been an update for A13 and some of the initial problems may have been solved. I don’t know as I haven’t read it.
Secondly here is a link showing options for upgrading your fairphone manually. Some of the options are without losing data, but I’d back everything up before deploying any of the options to be on the safe side.