I’ve also faced this issue. If your browser window is already maximised / full-screen before pressing “OK” on the experiment dialog box, the true ‘PsychoPy full-screen’ won’t initiate.
You can tell whether this process has failed or not based on whether you can still see the address / tabs at the top of the window. For some people this might not be an issue. But for me at least, it cuts off the top and bottom of my experiment page and users are unable to press the “Next” button to proceed.
Currently I plan to include an instruction to participants that tells them to ensure their browser is not maximised before they click the experiment link. I could move my “Next” button higher up on the page so that it’s still visible for those who do not follow this instruction - but, I think I may leave it where it is. This will ensure all my data comes from those viewing the experiment in true full-screen mode, as those who do not follow the instruction will not be able to proceed.