It seems entirely screwed - there isn't even a locking mechanism left it seems. What can I even do here without causing even more damage to the door frame?
That doesn't look like "fell apart". That looks like "was destroyed with a vengeance". You can try to grab onto what's left and pull sideways, but I can't even suggest what to pull as critical parts seem missing.
It used to look something like this:
#1 is what you have left (in part). It doesn't move, and therefore doesn't help you release the bolt (#3). #2 is the moveable bolt extension, which you'd normally just slide over to open the door.
You're going to have to find an angled pliers or similar and see if you can get it on the back of the actual bolt. There may be a small tab that used to engage a slide mechanism (#2, now gone).
The idea of pulling the hinge pins was floated in comments. The hinge pins are on the other side of this door. If access is available, sure, just pop them out with a hammer and a thin tool. Most aren't locked in place unless it's an outswing door.
Depending on the security level of the door, you may be able to detach it from its hinges and then remove it from the frame. Or detach the hinges from the frame or break the hinges into two by extracting the pin. After the door is off the hinges, you can extract the wrecked bolt by unscrewing it.
Ordinary hinges are cheaper than doors, and sometimes very crappy. High security hinges are expensive and hard to break (doh!), so it may be cheaper to destroy the door so you can re-use the hinges if all else fails.
A locksmith / security company employee may know some tricks.
It may be possible to (gently) remove the trim around the door, which could give some better access to the lock. For example, to allow access with pliers to the latch or ability to slide a credit card-like piece of plastic between the door to depress the latch. After removing the trim, you could also consider creating/cutting a gap at the edge of the door where it will be hidden by the trim. I replaced a couple of doors last year, removing and reusing the existing trim, so this should be possible on at least some doors. You probably want to have some matching paint available if you attempt this ...