Why do you say GPS is a "lie"? GPS is a thing not a statement.
If GPS is not working for you then I doubt if outdoor workouts will register anyway.
If all settings normal but behaviour is irrational there is a progressive hierarchy of remedies...
First force restart the Watch
i.e. press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo.
Then, although it may seem irrelevant, while it is restarting Force Restart the paired iphone Force restart iPhone – Apple Support (UK)
Test it for a while. If it is still misbehaving... Unpair and set up again
Unpair and erase your Apple Watch – Apple Support (UK)
and then
Set up your Apple Watch – Apple Support (UK)
You may also want to make sure the software on the watch and iphone are both up to date to the same level.
Update your iPhone or iPad - Apple Support. iOS16.3.1
Update your Apple Watch - Apple Support OS9.3.1
Make sure you are not using VPN or security apps on the iPhone.
If you've completed that troubleshooting and the issue is still not resolved, Contact Support.
Click here > Contact - Official Apple Support
or phone numbers
Click here > Contact Apple for support and service - Apple Support
and or
Genius Bar Reservation and Apple Support Options - Apple