Just got off the phone with apple support for this same issue: extended display mode not working after upgrading to iPadOS 16.4.1. Spoiler, was able to resolve issue (with caveat that issue might come back, and if it does, I need to let them know).
I found that when plugging into my Sceptre brand dumb-TV with any adapter/dongle/hub the extended display support was not working and the iPadPro would only mirror its display to the TV. We tried plugging my iPadPro into my home office setup, with a Dell WD19DCS dock and Dell P2415Q display, the extended display support worked just fine.
It was suggested to try clearing out the brains on the TV, similar to how you might clear out the SMC on a mac. I then did the following
Turned off the TV
unplugged the TV from the iPadPro
unplugged the TV power cord from the wall outlet
pressed and held the TV power button for greater than 10 seconds
plugged the TV power cord back into the wall outled
Turned on the TV
plugged the TV back into the iPadPro
Then, like magic, extended display support was working just like it was supposed to on the TV. After this I retested it with all my usual hubs and found them all to be working as they had before. The hubs/docks tested were:
ElGato thunderbolt 3 professional dock
Caldigit SoHo dock
Twelve South StayGo hub
Cable Creations usb c hub
Apple Digital AV adapter
Now mind you that this was a very surprising result, as the same docks and TV were still working just fine with a 2017 MacBook Pro, so it didn’t seem like the issue should have been related to the TV. Best we could figure is they just weren’t communicating correctly and resetting the TV made the iPadPro try its handshake a little differently (figuratively speaking). Maybe something was cached weirdly that made it act up after the iPadOS update.
So try resetting the memory on whatever display you are attempting to plug in to and that might just resolve your issue!