I would like to adjust the suggested route by clicking on the route and dragging it to e.g. another street to optimize the route (e.g. because I know as a resident, that driving through this street is actually faster etc.),
like it’s (partly) possible in Google Maps
The routing function on openstreetmap.org doesn’t support that, but there are plenty of third-party websites using OSM data that do.
This is one of them: