These are two different problems I encountered, when trying the same thing.
I can’t make a screenshot of the wrong file being added when doing drag and drop (first problem), so I can only elaborate on the second problem which is shown in the screenshot:
I want to add a song to the playlist called “Lana Del Rey lokal”, but this playlist is not available in the context menu. But it exists, you can see it in the list at the left above “Spielwiese”.
EDIT: I see that the playlist “Lana Del Rey lokal” is highlighted by a color. Maybe it is still “active” in a way, because I navigated through this playlist to the folder I am in in that screenshot (clicked on a different song of the same album which is already in the playlist).
in your screenshot you are already in “Lana Del Rey lokal” (this is why you see the name of the playlist in blue on the left). This is why you can’t add the song you have selected to this playlist as it is already in it.
You can be in the album but you accessed to this album through the playlist “Lana Del Rey lokal”. Can you click on Bibliothek on the left and try to access to this album in Bibliothek?