You need to double tap in the area where the battery is shown. Then it will toggle the battery visibility regardless of whether you are in full screen mode or not. You do need to be quite precise though.If I double tap the screen it goes into full screen mode - and yes, in full screen mode I can toggle between battery percentage on/off by double tapping. But it doesn’t show % when I go back to metrics mode.
As for distance discrepancy: previously it always showed the note “gps distance is xx shorter …” at the bottom of the workout on WOD for iPhone when you had the Pace tab selected. Now it no longer shows it - at first I was happy because I thought Apple fixed something in watchOS 9 and iOS 16, but no. In the Fitness app the distance is still off between pedometer and GPS though now WOD for some reason doesn’t show it anymore. I checked the GPS tab you mentioned, but it never showed it there in the first place.
The app only shows that message about the GPS distance being shorter/longer message when the distances differ by more than 10%. This is what it has always done, although it is phrased slightly differently (hopefully more clearly) than in previous versions.
As I say, to see the difference in distances go to the GPS tab and there is a GPS Dist metric which shows how much longer/shorter the GPS distance is than Apple's calibrated distance. Again, this has always been there, although in the latest version if the workout contains power data then you will need to specifically change the tab from showing Power to showing GPS.