I understand the need of terminal emulator for certain interactive programs, but inside Emacs I just use 'shell-command and output buffers. What's the benefit of having a terminal emulator inside the Emacs process? If the program is interactive (TUI) it won't integrate well with Emacs buffers/keybindings anyway right?

I haven't tried this project, but did switch to vterm from shell-mode a while back because it managed to fix most of the paper cuts when using shell-mode. I also used to create a lot of custom compilation buffers for things b/c it would create links to files that were helpful, but that has been less helpful to me. At the end of the day, there were papercuts that made shell-mode and compilation buffers less ideal and most folks were focusing on traditional terminal support.

My main use case is emacsclient and vterm as a terminal multiplexer, in place of something like tmux or screen.

But even locally I use vterm. A terminal is just text, why wouldn't I manipulate it with emacs? At any time you can switch to `copy-mode` and it behaves like a read-only text buffer that you can manipulate as you please.

None really. And for most cases, the included term is more than enough.