I have the same - got my 16 Pro on launch day (Sept 20), the message did appear and stay on for a day or so that "certain tasks related to the update continue in the background including indexing" as some people are saying, but it was gone by Sunday. It's Monday now, I woke up with 90% (that's the charging limit I manually set for myself), 2 hours later (after some light video watching of maybe 20 minutes during breakfast plus a 5 or so more minutes of texting at one point), and it's at 80%. Very odd.
IF the indexing is continuing without the message being displayed, ok, but how long does it approx. last for?
EDIT: the only thing that happened for me that was out of the ordinary - I initially wanted to transfer my old phone data via WiFi from the old iPhone 13 to the new 16 Pro, but both phones somehow lost WiFi-connection during the transfer, so I stopped that and tried launching the new phone again, this time downloading a back-up off of iCloud (which worked without a hitch). But somehow I can't see that having anything to do with battery drain, can it?