I'm using Switchbot at home to turn the lights on and off. There is an iOS app that does this via bluetooth. On the Pi there is homebridge and a switchbot host installed. When I use the app to switch the lights directly it almost works immediately even in the next room.
When I do it with the Pi via the switchbot host, I often have to send the signal several times until it works (to the next room more than 8 seconds). So I'm not sure if the problem is the strength of the bluetooth signal of the Pi or if the switchbot host program could be tweaked.