BTHome remote bluetooth

I’d like to use some BTHome protocol based sensors,
but my HomeAssistant is running in docker on a machine without bluetooth.
I have multiple Raspberry Pi-s in my home, and I’d like to use them to collect the BTHome messages and send them to HomeAssistant.

Is there any gateway / service I can run on a RaspberryPi to do this?

(I have not done this before. i’m just stating what I think is correct).
Simplest solution might be to get a device that has BTH proxy on it. LIke the new second generation Shelly plus (the ones with rgb) that have bluetooth built in and act as a remote (proxy) BTH host.

I am aware of that option, but I would like Raspberry Pi to act as Bluetooth Proxy. Is there any implementation?

Take a look at this and see if this is something you can modify. I used it earlier to have a raspberry pi scan my bluetooth plant sensors and report the data through mqtt.

Just buy an ESPHome Bluetooth proxy. They are $5 and they are very reliable, much more reliable than the Bluetooth stack on a Pi.

If you have ha running in a VM, use a bluetooth dongle on the pi and usbip. Connect to the usbip instance from your hypervisor and pass through to the VM. Relatively easy to set up, the home assistant instance sees it as local usb, and it’s useful to keep in mind for other usb devices, sensors, speakers, etc as well