what does built-in LiPo discharge protection look like?
The over discharge protection circuitry consists of two back to back power mosfets that open when the state of charge of the cell goes below a certain threshold.

When they are open, it is normal to measure a very low voltage at the cell terminals.  Also, it is normal that the voltage rises suddenly when you charge it since the protection circuitry is "untriggered" when you try to force a smallish current into the cell.

What I see as alarming is that 15 kOhm were enough to deplete the battery overnight. Either you were not using 15 kOhm, or the battery was nearly empty, or it actually is damaged.