I haven't tested that many Bluetooth devices but it seems to be per-device — e.g. my wired headphones are different than either of my Bluetooth speakers or the built-in speaker.

Apple's Shortcuts app supports a number of automation scenarios — for example, I would implement the feature you mentioned with a rule which tells Toggl to start an entry when my location is within a certain radius of work and stop it when I leave. You can also create or add to a note, send emails, etc. Since I have the Pythonista app, that could even extend to running arbitrary code.