This video details how to do it on the 1030 edge https://www.youtube.com/watch?v=7J2_WgRuo_g
On my 530 edge, once the komoot app is installed (via garmin IQ) and have synced the device to a phone or wifi – it can download the tours (aka routes!) you have saved to your komoot profile.
On my 530, I go to Menu -> Connect IQ -> Komoot: The first page has my planned tours in most recent order, and also a link to my profile so I can find tours in collections, highlights etc. Once you have found your tour, clicking “available offline” downloads it to your garmin, and it will be available in the Garmin Courses list, or available in komoot again without re-downloading it, ready for when you want to start the ride.
Hope that helps, you could export the GPX and import it into garmin connect, but that seems a little old school when komoot can do it for you.