Custom /prompts (#2696)

Adds custom `/prompts` to `~/.codex/prompts/<command>.md`.

<img width="239" height="107" alt="Screenshot 2025-08-25 at 6 22 42 PM"
src="https://github.com/user-attachments/assets/fe6ebbaa-1bf6-49d3-95f9-fdc53b752679"
/>

---

Details:

1. Adds `Op::ListCustomPrompts` to core.
2. Returns `ListCustomPromptsResponse` with list of `CustomPrompt`
(name, content).
3. TUI calls the operation on load, and populates the custom prompts
(excluding prompts that collide with builtins).
4. Selecting the custom prompt automatically sends the prompt to the
agent.

codex-rs/tui/src/bottom_pane/mod.rs

@@ -36,6 +36,7 @@ pub(crate) enum CancellationEvent {
 
 pub(crate) use chat_composer::ChatComposer;
 pub(crate) use chat_composer::InputResult;
+use codex_protocol::custom_prompts::CustomPrompt;
 
 use crate::status_indicator_widget::StatusIndicatorWidget;
 use approval_modal_view::ApprovalModalView;
@@ -336,6 +337,12 @@ impl BottomPane {
         self.request_redraw();
     }
 
+    /// Update custom prompts available for the slash popup.
+    pub(crate) fn set_custom_prompts(&mut self, prompts: Vec<CustomPrompt>) {
+        self.composer.set_custom_prompts(prompts);
+        self.request_redraw();
+    }
+
     pub(crate) fn composer_is_empty(&self) -> bool {
         self.composer.is_empty()
     }