Open with double-click/drag to icon without losing last session
The Continue last session option under Preferences-General gives no reason to believe that there might be restrictions on this behavior.
1) However, if you open a file by double-clicking or dragging it to the MuseScore icon,…
2) …only that file will be opened if Musescore is not already running.
There has been a lengthy discussion (https://musescore.org/en/comment/1063758) about this, with proponents and opponents of this behavior of MuseScore.
The fact is that everyone works differently, some with many open documents in parallel, others serially with one score after another score.
But negative consequences for MuseScore's current behavior exist only for the "parallel worker":
You lose your whole "workspace" when accidentally opening a file (when MuseScore is not yet running).
The Open recent menu entry are not a solution to this problem, because this list includes documents that have been closed in the meantime. Much older, still open documents, on the other hand, are no longer in this list.
To make both sides happy and to prevent the loss of larger sessions, a "Restore last session" should be added to the File menu:
If you then accidentally open a file and lose your last session, you can have it restored afterwards and those who don't want to have it restored just have to resist clicking "Restore last session".