I only got my FP4 a couple of weeks back and have not had time to play around with it that much, I had an LG G6 before that and it decided to break so I needed something quickly.
My biggest issue is that it seems that the FP4 camera is not supported that well in LOS. The best I seem to get is OpenCamera, where I can take 4000x3000 12MP photos, everything else seems to only take lower resolution pictures. The phone is supposed to have a 48MP camera. From what I've read though it seems the original software is a bit hacked together to acutally get 48MP out of the sensor... I have to admin I cannot compare to the original software, as the first thing I did when I got the phone was unlock the bootloader and install LOS.
As for the google bits, I tried very shortly without it, but quickly noticed google services are needed for many things so I just installed them by installing MindTheGapps. I haven't tried Netflix or Nebula though, so I don't know if widevine is working, and I do not have root.
On LineageOS 20 (android 13) I have the option of both the combined and the separate toggles, maybe you can configure it on your Pixel too?
I am on LineageOS 20 on a Fairphone 4 and just checked. It does indeed show this popup.
I've uninstalled the updates and just not updated just to get around the ads.. I would like to update it, but I'm not sure which launcher to switch to. What launcher would you recommend?