wearchronos.com seemed to hit my use case, but the reviews aren't great.
I had the first generation of Mi Band, the one with only 3 RGB LEDs, no display. And I loved it, I could easily see I have a new Gmail notification when it gently vibrated and the LEDs flashed red (well more of a breathe animation than a flash), or a Facebook Messenger one when it was blue. The Bluetooth communications it used made it easy to program your own vibrations and LEDs.
It sounds non intuitive but 90% of the time the flashing LEDs made me NOT check the phone. I was like, "oh blue, most likely my brother replied, I'll check it later"
I also fantasized about modding my current analog watch but fitting a tiny battery and a tiny BLE chip and a tiny vibration motor and surfacing tiny LEDs is way outside my possibilities. Chronos sounds good in theory but the end result is not what I want. I don't want to increase the thickness of my watch, or have to recharge it or worry about a magnet not staying in place.
You could actually log your food intake via their app. And sync data to your phone by removing the “cap” from the band and plugging it into your phone’s headphone port!
I think the general category you're looking for is devices that support ANT+.