I don’t know Zotero but it sounds like the links partially work? I’d guess they’re separate problems but maybe they’re connected.
I would start by finding out if Obisidian’s URI scheme (may also be called URL scheme) is registered with your Windows (I don’t know how to check this, so I’d search the Web first). If it’s not, then you’ll want to figure out how to change that. It it is registered, then the problem is elsewhere.