I've been using ghosty + ssh + mosh + tmux + claude code (sometimes codex) for a while now. It works well but the few things that still piss me off:
1. I have never been able to get copy-paste to work 100% of the time. I'm at about 95% of the time now which has been enough for me to not look into it.
2. Pasting and dragging and dropping non-text content (like images and videos).
At the end of the day I want it to feel like a native, local terminal
> I have never been able to get copy-paste to work 100% of the time
Have you tried Kitty? Its remote clipboard integration works over SSH, including images. Might be worth a look.