Battery Pinout: https://github.com/FrameworkComputer/Mainboard/blob/main/Electrical/Pinouts.md#battery-interface
You’ll probably need to dig through the EC code to figure what the data lines might be supplying: Search · battery · GitHub
If it hasn’t been documented, it looks like there’s some dedicated hardware/software for reversing laptop batteries: Hardware and Software Products - NIP Embedded Systems
and a corresponding community, eg…
https://www.laptopu.ro/community/laptop-battery-chip-reset-and-repair/hp-mu06-with-bq20z45-40-unlock-issue/
The Framework battery is a 15.4V nominal (4S) battery:
While it’s tempting to plug directly into the battery connector, to me it seems like it’d be a lot easier to just use USB-C PD - if you’re building your own case larger case, you might replace the lost USB-C with an additional de-shelled hub board even?