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.

Aside from physical dimensions, such rechargeable cells are specified by:

• Chemistry (LCO, LTO, LFP, etc.) LCO is the most common for older cells.
• Min and max operating voltage (those largely depend on the chemistry)
• Capacity (in A*h)
• Max charging and discharging currents. Those are usually proportional to the capacity for a given battery type, so they are often specified in relative units called C rate. A battery capable of 1C charge/discharge can be fully charged/discharged in 1 hour. 2C means 30 minutes, etc.
• Other parameters like temperature range which are less relevant in this case.

AFAIK there is no reasonable way to determine the parameters above for an unlabelled battery.