There is a solution for some (ex: my Xiaomi bluetooth scale) but not others.
However, should I install even one such app, I do not trust it will avoid listening to the BLE broadcast of data coming from other devices, and send it home.
Recently, this was a problem on the Wyze Watch which includes among other things a period tracker. I ended up replacing it by a Garmin eSports Watch: while the Wyze is a wonderful device (oh boy do I miss the puse oxymeter for O2 saturation...), it requires an app on the phone: if you uninstall it, the Wyze will work for a while... until it accumulates too much data.
After that, it presents various symptoms (ex: unable to pair) that end up with the touchscreen not working after a few month.
The Garmin can apparently be run autonomously and doesn't seem to have this problem (so far!) that seems to be cause by a lack of rollover/delete.
If it works as it should, with no app, I will replace it after a few months by a more advanced model like the Forerunner 945 that includes a pulse oximeter.
If it can't delete data on its own (without any phone pairing), I will look for another device that can work without a phone.
In any case, I will not let my health-related data be exfiltrated, even for something as innocent as a bluetooth toothbrush.
This article seems to support my almost luddite approach!