Doesn't Emacs fit that bill? In Emacs you can run terminal emulators and various shells and from all of them you can copy and paste into other buffers or from other buffers into them.
To add to this: I had lots of problems with Emacs terminal emulators until I switched to VTerm. Most things work like you’d expect in VTerm.
Yep, vterm is great. Only thing annoying me is, that I have to switch modes to copy anything. Wish it would work like `M-x shell` instead, where I can simply navigate upwards and when I move point back to the prompt, I can paste and continue with commands.