sport watch supported by Linux/FOSS software

Well, you can look at a gadgetbridge-compatible watch. gadgetbridge is a foss android app that replaces the manufacturer's app for snartwatches, earbuds, and a few other things. it's a good starting point, but most of the watches aren't directly foss. if you want a watch like that, you have two options. the pine64 pinetime is open source, but not easy to modify if you want a sealed, water resistant version. it also hasn't got the best specs. the bangle.js is a "hackable" smart watch, which has a a SWD interface on the outside, making it an easier option to modify. I can't say as much about it's fitness tracking, but it does have a heart rate monitor and accelerometer.