Successor software for Basecamp (no mobile app)

There is mapping capability on the Garmin Explore website (must be logged in).  https://explore.garmin.com/

The zumo XT2 is associated with an app called Tread for route creation but it will not run on a PC or Mac.

MyRoute-app has a mapping website.  It gets a lot of mentions as an alternative to Basecamp.   https://www.myrouteapp.com

BaseCamp is still available and can continue to be used, as can its predecessor MapSource. 

Garmin Explore has no Road Navigation capabilities, if I am not mistaken  (I use the Montana 700i).

I also tried MyRouteApp and with a GPX 1.2 Export I receive a usable route but without Viapoints.

You are right. Staying with Basecamp as long as possible seems to be the best option for my requirements.

Have you tried plotting a route in the free web app Plotaroute.com? You can export as a GPX track, then convert to a route in BaseCamp. You have to subscribe to get the satellite imaging and OS UK topo layers. 

Nakarte.me is another excellent free web app for plotting routes over a wide range of OSM, national topo maps and several satellite imaging layers, as well as Strava heatmap. One limitation is that it will not 'autoplot', which Plotaroute does.

Neither of these are where you would want to keep your library of tracks, routes and waypoints etc. BaseCamp is still an excellent tool which I use several times a week, but IMHO Nakarte and Plotaroute have the edge for route plotting - I often use them in combination before finally importing the GPX into BaseCamp and then onto my GPS device and phone.