I have identified an issue with skinning Edge in Windows 10 and 11. I follow the FAQ for skinning Edge and the first time I open Edge it is skinned. When I close Edge and later reopen it, it is no longer skinned. The is because MS by default is allowing Edge to run in the background (after closing) to cache it and make it open faster the next time.
To fix this problem so Edge will always be skinned each time you open it do the following:
Go to Edge Settings -> System and Performance and make sure Startup Boost and Continue running background extensions are both turned off. See picture.
This stops MS from running the Edge process in the background.