With the battery out we can take a closer look. That hole doesn't look so great, and probably has something to do with this not holding a charge.

The pack consists of standard 3.7V lithium cells in a 1S4P configuration. Capacity is not marked, but cell dimensions are 5.2x34x59 mm or 523459 in industry sizing.

I found some 523450 cells to rebuild the pack, which seem to work for now though capacity isn't great.

Note that rebuilding battery packs comes with the risk of personal injury, fire, and general bad juju, so read up on Li-Ion safety and pack construction before rebuilding your own.