Altitude acclimation is currently inactive. How do I turn this feature on? And what does it tell me?

Well, maybe you have to stay some days at altitude... If you have anything new I'll be glad to her it.

I'm looking forward to learn how that widget works

It takes into account 2 slightly different things:

the altitude at which you work out; and

the altitude at which you sleep (I think it checks the altitude at midnight).

As you have just arrived, I would fully expect the widget to show no acclimation at this stage.

support.garmin.com/.../

I am going on an easy hike with my wife today.  Let's see if this feature gets activated.  Stay tuned! 

Alright then.  I slept well last night at 10,400 ft. (all sensor features are fully on!)  And I am going on an easy hike with my wife today.  Crossing my fingers. 

As I recall altitude acclimation works 3,000 ft and above and may take 24 - 48 hours to show any acclimation.  Even 4 hours on a plane with a 6K cabin pressure won't do it.  Full acclimation will take many days/weeks depending on elevation. You will see the value increase daily eventually equalizing to a particular altitude.   Also upon returning home to lower levels the acclimation values will remain for days or weeks.