Replacing the battery in my electric toothbrush

I haven’t soldered anything since school. When we decluttered the flat some years ago, I gave away all the soldering gear of my dad. But this year, I finally soldered again. I upgraded my electric toothbrush with a much bigger battery, going from an aging 700 mAh to 2300 mAh. As we have three of those Braun / Oral-B Vitality (Pro) toothbrushes, I was thinking it might be worth it to try to repair one and see if I can replace or maybe even upgrade the battery. I had to recharge it every second day, and often it stopped working in the middle of my teeth-cleaning routine, which was getting very annoying. I could have bought a new toothbrush for something like 18 €, but instead decided to get a soldering iron. After some research I found the Pinecil v2, which is small and can be powered via USB-C, so it is not wasting too much space. Add to that a little soldering iron stand, a soldering pump, some desoldering braid, and, of course, solder. All together about 55 €. First, I opened the…