I tried this with InReach Mini on Android, but it wouldn't update. Earthmate up gave me a notification that new firmware is available, but it was nowhere to be seen in the app. Ended up just updating via computer. Maybe Mini doesn't support this?
According to the inReach Mini firmware update notes (https://support.garmin.com/?faq=ZGD1NiPQqL9Lma0Vy2ueL7), those updates must be installed through Garmin Express currently. This may be something that changes in the future but I don't have any specific information about when that change might happen or whether it would be available through bluetooth or not.