chore: fix all warnings; docs: require clean build

- Remove unused mut and dead code in TUI jump-back flow
- Update AGENTS.md to state build-fast.sh is the required check
  and all compiler warnings must be fixed

AGENTS.md

@@ -10,7 +10,8 @@ In the codex-rs folder where the rust code lives:
 
 Completion/build step
 
-- On completion of work, run only `./build-fast.sh` from the repo root. This script verifies file integrity and is the single required check right now.
+- Always validate using `./build-fast.sh` from the repo root. This is the single required check and must pass cleanly.
+- Policy: All errors AND all warnings must be fixed before you’re done. Treat any compiler warning as a failure and address it (rename unused vars with `_`, remove `mut`, delete dead code, etc.).
 - Do not run additional format/lint/test commands on completion (e.g., `just fmt`, `just fix`, `cargo test`) unless explicitly requested for a specific task.
 
 When making individual changes prefer running tests on individual files or projects first if asked, but otherwise rely on `./build-fast.sh` at the end.

codex-rs/tui/src/app.rs

@@ -803,7 +803,7 @@ impl App<'_> {
                                 // Replace widget with a new one bound to the forked conversation
                                 let session_conf = new_conv.session_configured.clone();
                                 let conv = new_conv.conversation.clone();
-                                let mut new_widget = ChatWidget::new_from_existing(
+                                let new_widget = ChatWidget::new_from_existing(
                                     cfg,
                                     conv,
                                     session_conf,

codex-rs/tui/src/chatwidget.rs

@@ -3702,18 +3702,6 @@ impl ChatWidget<'_> {
         self.bottom_pane.is_task_running()
     }
 
-    fn find_nth_last_user_cell_index(&self, nth: usize) -> Option<usize> {
-        if nth == 0 { return None; }
-        let mut count = 0usize;
-        for (idx, cell) in self.history_cells.iter().enumerate().rev() {
-            if cell.kind() == crate::history_cell::HistoryCellType::User {
-                count += 1;
-                if count == nth { return Some(idx); }
-            }
-        }
-        None
-    }
-
     // begin_jump_back no longer used: backend fork handles it.
 
     pub(crate) fn undo_jump_back(&mut self) {