> this appears to be native to the terminal, as in, there's no special application that runs or wraps an agent inside a tui

Same with codex? codex-rs at least, is a TUI as well, it does run a "app-server" in the background, that the TUI actually interacts with, but that's just an implementation detail. Also makes it easy to hook in your own programs to fire of codex "headless" sessions even without the TUI.