Yep, my mistake: I didn't number the pins of the chip correctly! SDA and SCL are pins 8 + 7, not 5 and 6! Not sure how I got that wrong, but it teaches me to double-check next time!
Luckily, the fuel gauge is the one component that's a bit optional – just nice to have!
Resoldering it on the board seems difficult, as it's so tiny! How would you approach that? I mean, I could try to cut the wrong traces, and solder teeny tiny wires to the chip? #electronics