MS Word does not have permission to open Word files after Ventura 13.3 update

I've recently updated my Mac to Ventura 13.3. Since then, I'm experiencing major problem with opening Word files from Finder. Some files can be opened without a problem, some just can't. To be honest, I'm absolutely sick of it, because Word is my daily driver that I use for my work. Clicking on the file just opens Word, but not the file. The file can be opened though directly through Word (File>Open>...). But when I edit it and try to save it, Word asks to grant permission for the file. When I grant it, it just doesn't work anyway. I'm forced to "create new file" by using the "save as" feature. I've already tried reinstalling the Office suite (Office 2019 btw.), but it's of no use. It's clearly caused by the macOS update. I've also spent many hours searching the web and trying variuos fixes, but nothing helps. Is anyone else experiencing this kind of difficulty? Any ideas how to fix this? Or do I have to just hope that the next Word/macOS update will fix this?