Google pixel 7A keeps turning off

As stated in the titular, my Google pixel 7A switches off periodically whenever it's not on charge. Even when I try to switch it back on, it won't work unless I've plugged my charger into the phone. When this does happen, periodically the battery will plummet wat below what it was originally. The back of my phone has also come off slightly, I think due to the heatwave (it appears glue has been used to stick it together). I'm just not really sure what to do from here, do I get the batteries replaced, do I get a new phone altogether?