Something where in the window for each connection I see local and remote contents and I can easily move things back and forth via whatever protocol I need.

Yes, I can do this via a terminal or Fetch or FileZilla technically but they all dont work perfect.

Or maybe instead of a window for each connection a single window with a 'tab' for each connection I have open.

I usually have a lot of sessions open and switching between the terminal and Fetch is just a nightmare.