Plug three holes in Servo input forwarding

1. Scroll no longer wipes keyboard focus. Servo holds DOM focus across
   wheel events; the shell was clearing keyboard_focus and typed_texts
   on every scroll, so a focused input went deaf the moment the user
   scrolled. Scroll still drops the buffered click point because that
   coordinate is captured against the pre-scroll viewport.

2. Mouse-down hands focus to the shell's root focus handle (in
   addition to mouse-up's existing click forwarding). The user can now
   start typing the moment they press the page, instead of having to
   first complete a click round-trip to escape the omnibar's focus.

3. Sidecar hover() honors the requesting webview_id instead of
   defaulting to the first webview in the map, so multi-tab sidecars
   no longer pipe every hover into tab #1.

crates/ely_app/src/shell/web_surface.rs

@@ -137,9 +137,13 @@ impl WebSurfaceStore {
             .entry(tab_id.clone())
             .and_modify(|current| *current = current.combined_with(delta))
             .or_insert(delta);
+        // Drop any buffered click — its viewport coordinates were
+        // captured against the pre-scroll page, so applying it after
+        // the scroll would land on the wrong DOM element. Keep
+        // `keyboard_focus` and `typed_texts` though: Servo maintains
+        // its own DOM focus across scrolls, so a focused input keeps
+        // accepting the user's keystrokes after they wheel-scroll.
         self.click_points.remove(tab_id);
-        self.typed_texts.remove(tab_id);
-        self.keyboard_focus = None;
         true
     }
 

crates/ely_app/src/shell/web_surface_controller.rs

@@ -96,6 +96,14 @@ impl ElyShell {
         }
     }
 
+    /// Hand focus to the shell's root focus handle so subsequent
+    /// keystrokes route to the web surface. Called on the very first
+    /// mouse-down inside an external page so the user can start
+    /// typing without waiting for the click to fully resolve.
+    pub(super) fn focus_web_surface(&self, window: &mut gpui::Window) {
+        self.focus_handle.focus(window);
+    }
+
     pub(super) fn type_text_in_external_web_viewport(
         &mut self,
         tab_id: TabId,

crates/ely_app/src/shell/web_surface_view.rs

@@ -90,6 +90,7 @@ fn render_input_overlay(
     url: String,
     state_entity: Entity<ElyShell>,
 ) -> impl IntoElement {
+    let down_entity = state_entity.clone();
     let click_tab_id = tab_id.clone();
     let click_url = url.clone();
     let click_entity = state_entity.clone();
@@ -103,6 +104,16 @@ fn render_input_overlay(
         .absolute()
         .size_full()
         .occlude()
+        // Mouse-down hands focus to the shell's root focus handle so
+        // subsequent keystrokes route to the web surface instead of
+        // the omnibar Input. Doing this on mouse-down (not mouse-up)
+        // lets the user start typing as soon as they press, matching
+        // native browser focus semantics.
+        .on_mouse_down(MouseButton::Left, move |_event, window, cx| {
+            down_entity.update(cx, |shell, _cx| {
+                shell.focus_web_surface(window);
+            });
+        })
         .capture_any_mouse_up(move |event, window, cx| {
             if event.button != MouseButton::Left {
                 return;