Edit: Scratch that. It worked for less than 24 hours and went back to not connecting again.
To answer my own question, I hadn't updated the firmware on my printer as it has been working fine so I just didn't see a need to.
Went ahead and updated just in case and voila it started working.
Looks like Bambu is locking that functionality down behind the firmware version. As I didn't see any notes in the update log pertaining to the camera so that's the only thing that comes to mind.
There are some tools out there to rip the DRM out of those.