Dgrant your battery example is wrong. Series adds voltage but mah remains as one cell. Parallel capacity mah adds up but voltage remains as one cell.

https://zbattery.com/Connecting-Batt...es-or-Parallel

In my setup I have two 3s packs. Each pack 9.9. volts 2500 mah. With the special connector the 2 packs are wired in series so I have 19.8 volts but still 2500 mah. Life batteries last a long time for me. I did manage to run the setup down to minimum voltage. I thought I ruined the packs but they charged up with out a problem. If you have an individual battery in a pack that does not balance out you can make a connector to charge up that one battery. I’ve not had to do that.

In my case I soldered the battery packs. As pointed out you have to be quick with the soldering. Not too much heat for too long. But is can be done. I’m looking at making a spot welder for battery packs. My first attempt was a failure I used a cheap solenoid. Will try again.

I have looked at store bought packs and I can make the packs cheaper than store bought. Maybe not as pretty. I’m a tinkerer so I do things like this. I would not do this with a Lipo battery. I don’t know if they even sell Lipo cells.