Is it possible to add a marker to a strip in the VSE? I don't want to add the marker to the timeline with m, but to the selected strip, e.g. to mark possible cut positions to choose from. Something like this:
No, video-editor strips don't have their own markers.
One workaround for this is to cut the strip soft. Place the green time cursor where you might want to cut, then hit K. By selecting both ends of the cut, you can move the cut around, since both strips keep their original length under the hood.
Until you delete or move one of the strips, the cut is not noticable. and you can always restor one of them to full length.