Go to Device Care in your Settings. Then go to Battery and finally Battery Usage. It should tell you what apps are using the most battery. And it could well be FB. I found my phone was eating more battery after the Pie update also, and found that Gas Buddy was the culprit. I set the app to sleep, set it so it could not use background data and even force closed it. But it started itself right back up every time. It has been a pest in the past in the same ways.
I only need the app a few times a year, so I just uninstalled it for now. Maybe they'll have it fixed by the time I need it again.