transcript-ui: build_tree, the screen without claiming the window root (RUST.md's E4)

build() always finished by calling ui_state.set_root(), which is right for
a window that *is* the transcript screen and wrong for a caller embedding
it beside something else (the desktop app's session list). build_tree()
is build() minus that last step, returning the widget tree instead of
planting it; build() is now one line on top of it, so nothing else
changes for existing callers.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

iris/transcript-ui/src/lib.rs

@@ -88,6 +88,25 @@ pub fn build<Rsc: HasEvents>(
     ui_state: &mut impl HasRoot,
     rows: Vec<FoldedRow>,
 ) -> TranscriptScreen
+where
+    Rsc::State: FocusHost,
+{
+    let (screen, tree) = build_tree(rsc, rows);
+    ui_state.set_root(tree);
+    screen
+}
+
+/// The same widget tree [`build`] makes, without claiming the window's
+/// whole root -- what a caller embedding this screen alongside something
+/// else of its own needs (RUST.md's E4: a session list beside the
+/// transcript on the desktop). `build` is `build_tree` plus
+/// `ui_state.set_root(tree)`; kept as its own function since most callers
+/// (the winit example, an eventual Android cdylib) want the screen to *be*
+/// the window and don't need the strong handle back.
+pub fn build_tree<Rsc: HasEvents>(
+    rsc: &mut Rsc,
+    rows: Vec<FoldedRow>,
+) -> (TranscriptScreen, StrongWidget)
 where
     Rsc::State: FocusHost,
 {
@@ -111,13 +130,17 @@ where
 
     let (composer, composer_bar) = composer::build_composer(rsc);
 
-    (list.width(rest(1)).height(rest(1)), composer_bar)
+    let tree = (list.width(rest(1)).height(rest(1)), composer_bar)
         .span(Dir::DOWN)
-        .set_root(rsc, ui_state);
+        .add_strong(rsc)
+        .any();
 
-    TranscriptScreen {
-        list,
-        composer,
-        selection,
-    }
+    (
+        TranscriptScreen {
+            list,
+            composer,
+            selection,
+        },
+        tree,
+    )
 }