If you don't want people calling these apps TUIs, what would you prefer people call them? And what does the term TUI refer to, if not this?
A more textually oriented environment (like a normal Unix shell) is, in my experience, usually referred to as a CLI: Command Line Interface.
I did find an interesting hybrid in the Pi coding agent: it seems to leverage the normal terminal scrollback, while still enhancing it with things like transient input fields and status lines, so that it can display those without cluttering scrollback.
I see TUI as a more general term: a program based in a terminal.
In my mind it does not imply it has to be an ASCII GUI style thing and not just a stream oriented non-interactive program.