Feature request bluetooth / offline mode?

Wow, ok, that is strange. And I tried it here and it's fine.

One thing that could be an issue - I saw you mentioned you were on firmware 2v13.123? Maybe try and update to latest again? 2v13.123 did have an issue that could cause some code to fail, and if the boot code failed before NRF.sleep() was called the Bangle wouldn't stop advertising.

... although I'd have thought if you were connected with the IDE you'd have seen some errors in the console.

Is it possible that there is some scheduling that reactivates bluetooth after a while?

Not by default, but what apps do you have installed? You can get a list from the App Loader's More... menu

It's entirely possible one of those would try and wake up bluetooth.