Airplane mode : bug ?

You sure? The manual states:

Airplane Mode

Select to enable or disable airplane mode to turn off all wireless communications

Did you check if it was still in airplane mode? Did you connect it to computer with garmin express installed?

Could also be that airplane mode has a time-out functionality or act like like iphone (disabling BT in controlpanel doesn't actually disable BT, you have to do that in settings, it just disconnect all connected devices till next morning [exept Apple Watch]).

I did different tests. the BT and the wifi are well deactivated on the Epic and the airplane mode activated. And the training is well sent to my iPhone. Second test by also disabling BT on the iphone. The workout is successfully sent to Connect Garmin. So I think it is done by wifi.

And in my Garmin Connect Connectivity settings I selected Auto Download.

So I redid the test by disabling automatic download in the wifi tab, and nothing is transmitted

CONCLUSION : Automatic download via wifi takes priority and works even if airplane mode is activated

Yep, pretty certain. I believe it's poor wording in the user manual. Would need to get an answer from Garmin about what is actually disconnected when Airplane Mode is enabled but 99.999999% certain that BT will remain active.

Smartphones are the similar; when put in Airplane mode BT generally remains active, WiFi might or might not be disconnected but cellular connection is definitely blocked. Apple brought this mode of action in way back in iOS11 such that only connection to the cellular network is blocked in Airplane Mode. 

When I turn on airplane mode on my Epix 2, BT, Wifi etc. are displayed as "off", which is weird. Curious stuff. 

Same here. BT is OFF.
I always use Airplane Mode when I want to save some battery without engaging the Battery Saver mode.
And it works: no weather report for example and no messaging...