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you can't reprogram it from the charge cable
Unless the middle pins melted away from your sweat over time you definitely can, it is standard SWD so any SWD debug dongle works, even the charging cable has all 4 wires there going to usb data pins so simple usb female to 4 jumper wire adapter + swd dongle does the job, I did it many times.
EDIT:
By SWD dongle I mean ~US$2 thing like this https://www.aliexpress.com/item/1005001621626894.html or this https://www.aliexpress.com/item/1005005002268447.html or even just raspberry pico loaded with some DAPLink implementation (there is plenty of them) -
As fanoush mentioned, you definitely can. Being able to reprogram the watch was one of the reasons I bacled the kickstarter, because the watch is opened up to all kinds of firmware without having to sacrifice waterproofness. I've tried it as well (had a female usb connector soldered onto some protoboard and broke out the pins to a j-link adapter)
@fanoush I wonder if the usb/swd cable can be used for installing the DFU and maybe factory reset the watch? Or maybe even run a small diagnostic that gathers data on the watch as well as some data on the responsiveness of the peripherals. Might help with troubleshooting in the future.
From what you've said I think I won't have much more luck connecting it than you. If I could program it using the charge cable connected to my laptop I'd probably buy it (although maybe not for 30€) - but I don't think that's possible.