Chosen Solution

Battery dies in minutes despite being fully charged. Can the battery be replaced? If so, where can I get that done?

See step #11 of the teardown: GoPro Hero4 Session Teardown

I have watched other videos of successful disassembly without destroying it, it’s totally possible to replace the battery although sourcing a replacement specific to the gopro is difficult, they use a 1s 3.7v 1000mah lithium cell. One can be found relatively cheap that will fit.

New session batteries: https://www.aliexpress.com/item/10050019