If you open a message in a new window in the classic theme, it will have a different display design than the current one.
I agree about the edit and delete buttons being like in the old design — and probably the share/report options could be moved there too. Through the same "..." block, for example, since these features aren't used too actively.
What's actually missing when you click on a user's name is "send a private message." I think there was also "ignore" and some other old features, but I can't recall them anymore, so they probably weren't that necessary.