Suggestion: integrate elevation gain into walking or create a hiking activity for the vivoactive4

Thanks a lot! That was super helpful. It’s my first Garmin and I’m therefore still a bit lost in the function-jungle.

If you go to Garmin Connect Web and open one of your activities with GPS you will see a section.

vívoactive 4
Software: 6.90
Elev Corrections :(?)  Disabled

Hover the cursor over the question mark and you will see this:
"Instead of the data from yout device. If your device has a barometric altimeter Elvation Correctiosn are disabled by default"

Don't know what it changes because I've never tried..

If you enable elevation correction, the altitude will be taken from a map instead of what was measured by the watch.

Yes, but that is not the same as elevation gain, which is what the poster was asking - I think.

As a side note, what watches do record elevation gain? I thought they only show elevation (altitude).

Most watches will add up the elevation gained during an activity at least after you are finished. 
The Vivoactive series has "total ascent" and "total descent" available as data fields during activities. 

See Hike2+ https://apps.garmin.com/en-US/apps/116a5b59-29ae-4397-a70e-907d7e5f8e44

There you can see elevation, a history of elevation, Ascent, Descent, etc  As well as other things like the weather, sunrise/set.  About 12 pages of data.