assistant2: Fix inline context picker and handle dismiss (#23081)

The new `ContextMenu`-based `ContextPicker` requires initialization when
opened, but we were only doing this for the `ContextStrip` picker, not
the inline one.

Additionally, because we have a wrapper element around ContextMenu, we
need to propagate the `DismissEvent` so that it properly closes when
Escape is pressed.

Release Notes:

- N/A

crates/assistant2/src/context_strip.rs

@@ -168,7 +168,7 @@ impl Render for ContextStrip {
                 PopoverMenu::new("context-picker")
                     .menu(move |cx| {
                         context_picker.update(cx, |this, cx| {
-                            this.reset_mode(cx);
+                            this.init(cx);
                         });
 
                         Some(context_picker.clone())