I had the upgrade to Android 13 earlier this week. I had absolutely no problems at all. In fact feels smoother and battery life feels improved. I suggest before you get the upgrade clear cache and any storage on your device. I read on here people having issues, personally no problems at all.. I felt same too, so I did what I suggested before the update it's been great..
DON'T upgrade! If you wait, wait for at least 2 months.
The term "bleed edge" is often said for a reason.
If you decide to ahead, then absolutely make sure everything, I mean everyone important is backed up. Double, no triple check that backups exist. I've notice somethings aren't backed up, and can't be.
Read some of the other posts of issues experienced and then decide.