Wall Mount TV to Drywall with Backing (Without Studs)

Not terribly common, but common enough. There are a couple or more reasons for this configuration. My main understanding is that attached Condos are between Commercial and Residential construction, but not purely one.

The plywood could be satisfying a Durability Requirement from the Commercial side, while the Fire Resistance of both is satisfied by the Drywall. It could also be a poor attempt at blocking for wrongly hung drywall. Though lame, it's literally light-years beyond the entirety of "expert" and "professional" drywall installers.

Concerning your Snap Toggles, I'd nip the plastic head off the end and use the legs to splay them right. Or, a straightened paper clip could coax the toggle to toggle correctly. BUT, pictures 1 and 3 look like you're drilled into studs and your Snap Toggles would only ever work in just picture 2's openness.

If all of that fails, then I think your best bet is the good old Hollow Wall Anchor pictured below. It's a bit weaker than a Wing Toggle but can work perfectly well in all of your pictures' situations. Here's a video to explain that you need LONGS instead of shorts and how they operate. How To Use Hollow Wall Anchors https://www.youtube.com/watch?v=nNFv65-QTPI