[codex] Remove unused Rust helpers (#17146)

## Summary

Removes high-confidence unused Rust helper functions and exports across
`codex-tui`, `codex-shell-command`, and utility crates.

The cleanup includes dead TUI helper methods, unused
path/string/elapsed/fuzzy-match utilities, an unused Windows PowerShell
lookup helper, and the unused terminal palette version counter. This
keeps the remaining public surface smaller without changing behavior.

## Validation

- `just fmt`
- `cargo test -p codex-tui -p codex-shell-command -p codex-utils-elapsed
-p codex-utils-fuzzy-match -p codex-utils-string -p codex-utils-path`
- `just fix -p codex-tui -p codex-shell-command -p codex-utils-elapsed
-p codex-utils-fuzzy-match -p codex-utils-string -p codex-utils-path`
- `git diff --check`

codex-rs/utils/path-utils/src/env.rs

@@ -1,9 +1,5 @@
 //! Functions for environment detection that need to be shared across crates.
 
-fn env_var_set(key: &str) -> bool {
-    std::env::var(key).is_ok_and(|v| !v.trim().is_empty())
-}
-
 /// Returns true if the current process is running under Windows Subsystem for Linux.
 pub fn is_wsl() -> bool {
     #[cfg(target_os = "linux")]
@@ -21,26 +17,3 @@ pub fn is_wsl() -> bool {
         false
     }
 }
-
-/// Returns true when Codex is likely running in an environment without a usable GUI.
-///
-/// This is intentionally conservative and is used by frontends to avoid flows that would try to
-/// open a browser (e.g. device-code auth fallback).
-pub fn is_headless_environment() -> bool {
-    if env_var_set("CI")
-        || env_var_set("SSH_CONNECTION")
-        || env_var_set("SSH_CLIENT")
-        || env_var_set("SSH_TTY")
-    {
-        return true;
-    }
-
-    #[cfg(target_os = "linux")]
-    {
-        if !env_var_set("DISPLAY") && !env_var_set("WAYLAND_DISPLAY") {
-            return true;
-        }
-    }
-
-    false
-}

codex-rs/utils/path-utils/src/lib.rs

@@ -1,7 +1,6 @@
 //! Path normalization, symlink resolution, and atomic writes shared across Codex crates.
 
 pub(crate) mod env;
-pub use env::is_headless_environment;
 pub use env::is_wsl;
 
 use codex_utils_absolute_path::AbsolutePathBuf;