Identify this rechargeable battery pack
It looks like one of a standard Li-Ion or Li-Po pouch cells,  size 5.0 x 33 x 55 mm, more like 50 mm, or 503350 for short notations, could be 503250. An example from Adafruit of a 503035 battery:



The example has h=5mm, w=30mm, and L=35mm

To see the actual label and determine the size, you need to carefully remove the blue wrap and exclude battery protection part from measuring.

CORRECTION: the battery protection part is included into length measurement.