Whoever wrote https://didac.dev/blog/i-made-my-withings-scale-sync-to-home... apparently got it working with Bluetooth LE and an esp32 chip. Sadly, they didn’t share their code yet, and as I lack their social media options I can’t email them requesting they post it. Perhaps they’ll see this comment, or perhaps someone else will repeat the solution and post it this time — but without the HealthKit path, there’s not much gain to be had over just manually typing the weight measured into the Health app.

Looks like the Body+ and WS-30 models have an official “Bluetooth networking mode,” but alas, my model does not.