I typically just create a "new" connection in a separate tab when I want to add tunneling.

I put new in quotes because I use another little-known feature, "ControlMaster". Multiplexes multiple connections into one, it makes making " new" sessions instant (can also be configured to persist a bit after disconnecting). Also useful for tab-completing remote paths. It does not prompt for authentication again, though. And it's a bit annoying when the connection hands (can be solved with ssh -o close, IIRC).

TIL; thanks, that's interesting (and somehow escaped my 20+ years of using ssh)! As usual the gold is in the comments :-)