Strava syncs to your Garmin Connect account which in turn is the thing that talks to your Edge.
I’ve got the Edge Explore 2 as well and it’s spot on. Create route on Strava (laptop or phone), turn on Garmin and the route appears in a few moments.
Your Strava account needs to talk to the Connect one, there’s somewhere in the permissions for both where you just put in the “yes, I want to sync” and it’ll take care of it all. Then whatever you do on Strava will appear on Connect and then on Garmin. Same in reverse too – hit Save on the Garmin at the end of a ride, it’ll upload to Connect and then push it to Strava.
I hate Connect, the only purpose it serves it to push things to and from Strava which is where I create and save all my routes.
To upload an external GPX (on the website) go to Create Route and click the little upload button top left. Not sure on phone app – quite honestly the Strava website and app seem to have been written by two completely different teams, neither of whom have ever met!