Thank you @ndiaga for the idea, unfortunately, no luck as friendly URLs were already disabled. Turning on didn't help either, except for some more ERROR 500 issues in the backend (we had never had any issues with Wordpress backend, but Prestashop keeps logging out all the time or displaying errors in the backend daily). It is indeed strange that some parts of the website work, while others show an empty page.
Another idea we had is that maybe the problem appeared after we removed one of the languages. That's the only thing the debugger shows, missing translations. But all the products are set to English and the shop is set to English, setting up Polish one more time with dummy products also didn't work, they don't show up.
At this point, we are pretty desperate and will most likely delete the whole shop and set it up again one more time. If anyone had more ideas how can we avoid this or troubleshoot we will be extremely grateful!