Remove the legacy TUI split (#15922)

This is the part 1 of 2 PRs that will delete the `tui` /
`tui_app_server` split. This part simply deletes the existing `tui`
directory and marks the `tui_app_server` feature flag as removed. I left
the `tui_app_server` feature flag in place for now so its presence
doesn't result in an error. It is simply ignored.

Part 2 will rename the `tui_app_server` directory `tui`. I did this as
two parts to reduce visible code churn.

docs/tui-alternate-screen.md

@@ -75,7 +75,7 @@ let terminal_info = codex_core::terminal::terminal_info();
 !matches!(terminal_info.multiplexer, Some(Multiplexer::Zellij { .. }))
 ```
 
-This detection happens in the helper function `determine_alt_screen_mode()` in `codex-rs/tui/src/lib.rs`.
+This detection happens in the helper function `determine_alt_screen_mode()` in `codex-rs/tui_app_server/src/lib.rs`.
 
 ### Configuration Schema