As others have said, your pad is gone. If you’re struggling to expose the trace needed to solder, it might be easier to find out which one of those test points corresponds to the battery terminal and solder a wire to that instead.

Here’s a great resource I used to repair an Xbox one controller after destroying the pads in an attempt to replace an analogue stick.

As I understand it, their main benefit is in aiding alignment rather than for strength.

Yeah, one thing I remember from visiting Vienna was how proud people seemed to be of the tap water (and it was indeed nice).