One option is espresence
https://espresense.com/. Esp32 based Bluetooth trancievers
Another is room assistant Introduction | room-assistant (similar but pi instead of esp - unknown if it’s still being developed, last update on the site is 2022.)
You can use esp32 Bluetooth products xiws with Bermuda
Or you could roll your own automations and the iBeacon integration.
Theres plenty other options but these should get you started on what you’re looking for.
And yes these all should run on HAOS because they’re either HACS custom components or automations on existing tech or addons available in the addon store.