The Apple part number (MPN) for the board that this PRAM is connected to inside an A1138 PowerBook is 820-1819-A.
The MPN for the board inside an A1107 PowerBook is 820-1814-A.
The only available Li-Po battery replacement I can find with the required 2-pin connector already attached to the wires is the CS-AP1107SL by Cameron Sino. However, this battery is marketed as compatible with the A1107 or more generally with the 17-inch PowerBooks.
I wonder why it is not also marketed as compatible with the A1138. According to https://www.smallbattery.company.org.uk/... the LP302030 battery is used on both 820-1819-A and 820-1814-A boards.
While the boards may be different, I think that the rectangular 3.7 V Li-Po battery packs can be used in any 15-inch and 17-inch PowerBook.