agent_ui: Clear original agent prompt when creating a new worktree (#51839)

Before you mark this PR as ready for review, make sure that you have:
- [x] Added a solid test coverage and/or screenshots from doing manual
testing
- [x] Done a self-review taking into account security and performance
aspects
- [x] Aligned any UI changes with the [UI
checklist](https://github.com/zed-industries/zed/blob/main/CONTRIBUTING.md#uiux-checklist)

Release Notes:

- N/A

crates/agent_ui/src/agent_panel.rs

@@ -3021,8 +3021,17 @@ impl AgentPanel {
             multi_workspace.activate(new_workspace.clone(), cx);
         })?;
 
-        this.update_in(cx, |this, _window, cx| {
+        this.update_in(cx, |this, window, cx| {
             this.worktree_creation_status = None;
+
+            if let Some(thread_view) = this.active_thread_view(cx) {
+                thread_view.update(cx, |thread_view, cx| {
+                    thread_view
+                        .message_editor
+                        .update(cx, |editor, cx| editor.clear(window, cx));
+                });
+            }
+
             cx.notify();
         })?;