Hi,
Whilst it may have the same battery type (or series? perhaps) number i.e. L15M3PB0, the replacement battery hasn’t got the same Lenovo battery part number.
Assuming the original battery is the one shown connected to the motherboard in the 1st image, then on the barcode label it has the part number beginning with 8S5B10M49824——— ——.
The 5B10M49824 corresponds with the part number for one of the batteries (item #13 Lenovo ideapad FLEX 5- 1570 column) shown on p.72 in the hardware maintenance manual for the laptop and also what is shown for one of the 3 compatible batteries in the parts list as well (click on Select Commodity > Rechargeable batteries and Internal (3).
Your replacement battery part number is 8S5B10K84494 ———, and it is not listed for this laptop model. Searching online using this part number (omit the 8S from the beginning and search using 5B10K84494) shows what models it may be used on. (I say may because perhaps it may not be. The seller may be relying on the type number as you did and for other batteries at least is usually correct. The parts list for the mentioned device may need to be checked to verify. )
I don’t know why both the batteries have the same type (or series) number, as you would think then that they would be identical. Also if they were the same then why not have the same part number as well??
Given the above, it may be prudent to search using the specific Lenovo part number when looking for Lenovo parts.