@sudachi_se
I have heard of others who have similar problems where the puzzle slider popup appears, but the background of the puzzle does not, making it impossible to position the puzzle piece correctly.
Do you see three buttons at the bottom of the puzzle popup? One should should close the puzzle, one should reload the puzzle, and one should provide an audio alternative that requires you to enter spoken numbers to solve. Try all of those if you can.
You might try disabling your ad blocker (or other extensions) temporarily to see if that allows the puzzle to appear correctly. If you are able to sign in when using a private browsing session, that might indicate the problem is related to your temporary internet files or eBay cookies -- it might be worth trying to clear those. Note that if you clear your cookies routinely you face a higher chance of going through strict verification when signing back in.
After you have signed in successfully and updated your eBay cookies, after a while you should no longer need to go through strict verification every time. After a week or two of going through verification every time to sign in, the only time I see a puzzle slider now is when I sign in or out using Firefox on my phone, which I rarely do.
Another thing to try: instead of signing in the normal way, try adding an item to your Watch List -- you should be prompted to sign in if you are not already signed in, but the dependencies are different and you may be able to avoid verification that way (until eBay notices and fixes this, at least).
