Have you already disabled background app refresh for the FB app? I had this issue the first week where it was churning all night, making my phone hot. Once I disabled background app refresh, it stopped.
One thing to note, this is from at least iOS 15, if not even older but don't leave the FB app open all the time. Actually close it completely from the switcher. It seems to get around some privacy settings if the app is always running in the switcher. Of course, I am sure it is running something no matter what, once installed, but ...