After days of researching, I think I got what happened.
The basic should be clear: route from Strava, segment functions on, etc. The point is there is something wrong with routes from Strava. Garmin receives starred routes from Strava, and here is the tricky part: loads segments from routes, not from Edge. It means when you create a route with segment you want, Strava is responsible of preparing those, not Edge. So we need to know why segments are not on routes from Strava side.
So ideally, you star a segment, then create a route covering that segment so Strava knows which starred segment you want on that route, finally star the route to sync. It's simple to check if the routes synced are with segments: check if there are segment_start and segment_end waypoints of your route on Connect.
There is a bug on Strava side: after creating the route, Strava fails to immediately match the starred segment to that route, causing no waypoints sync to Connect. The way to solve this is simple: unstar the route on Strava and clear the synced old route on Connect, then restar the Strava route. Check segment waypoints on Connect. If no, redo this step. You should now find the segment function works fine when following a route on Strava.
You must have the segment starred before creating routes on Strava. Clear the synced old route on Connect every time to make sure your route list is neat.
Your last comment is right. The thing is that before this bug everything went good and it just confuses everyone.
Today I was able to visualize a Strava Segment after Starring a route and loaded into Connect.
How can I visualize Segments if I am not following a course? as said before, it worked in that way but particuarly a segment doesn't start if I ride throughout it. Normally I am riding and following a course and when I go over that segment I pause and stop the navigation but it does not start.
