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 &quot;expert&quot; and &quot;professional&quot; 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