> Konsole is way faster than any of those on my computer and it has all the usual suspects I'd expect from a modern terminal emulator.

Same boat here, though I also get to enjoy some of the benefits of libghostty, via ghostel in Emacs. Ghostel is noticeably faster when there's a lot of output being dumped, but I don't often need the speed and use it only because it's integrated rather well into the rest of my Emacs.

> tmux -CC integration

If you can stomach Emacs, there are at least two packages that implement this, one via eat and another via vterm, though none via ghostel just yet. Shouldn't be difficult to port, though.