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Maybe try it with a different browser or in a incognito mode? Maybe you have some browser extensions installed which interfere with Facebook?

Are there any error messages along the way? Is the Use as profile photo button dissabled, or clickable, but simply does not do anything?

Yes. I will now try to disable all extensions and ad blockers. Apparently, this is the case? And then I'll write.
Thank!

And here is the result...

1.jpg

Something is not right, but what exactly I cannot understand?

I don't really know too. Everything seems fine from the screenshot that you provided. The big blue button button should apply the change.

As a last resort, you could try to open the Chrome console and see if there are any errors or other messages printed out there when you try to apply the photo frame.