Newbie Adhesive Question
The solder broke. That is likely to happen if there's mechanical stress on the solder alone … as in this case.

While you could try to repair that yourself with a hot air pistol, I recommend to take that piece to a repair cafe and let someone do it who does this all the time. The difference between repaired and gone forever is about 10 seconds, or 10 millimeters.

I also think this design is pretty shitty, as there is always mechanical stress on a charging connector. This connector wasn't intended for that use but for contacting a battery instead. Proper connectors for mechanical stress have additional tabs at least, if not bolt holes.

These are just pogopins on a spacer, it seems. They are intended for lab use …