Chrome: turning the File tab off closes a Backstage that is already open

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

crates/ui-egui/src/lib.rs

@@ -1129,6 +1129,10 @@ impl SheetApp {
         // The language the widgets translate with this frame (see `i18n::current`).
         i18n::set_current(&ctx, self.ui.language);
         let t = theme::Tokens::get(&ctx);
+        // A host can turn the File tab off while Backstage is already open: close it.
+        if !self.chrome.file_tab {
+            self.backstage = None;
+        }
         if self.backstage.is_none() {
             self.ribbon_keys(&ctx);
         }

crates/ui-egui/tests/host_chrome.rs

@@ -52,3 +52,14 @@ fn without_the_file_tab_the_backstage_view_never_opens() {
     assert!(h.state().backstage.is_none(), "so is every page, Print and Save As included");
     assert!(h.query_by_label("AutoSave").is_some(), "the title bar can stay on its own");
 }
+
+#[test]
+fn turning_the_file_tab_off_closes_an_open_backstage() {
+    let mut h = harness(Chrome::default());
+    h.state_mut().open_backstage(Page::Home);
+    h.run_steps(3);
+    assert!(h.state().backstage.is_some(), "Backstage opens with the File tab on");
+    h.state_mut().chrome.file_tab = false;
+    h.run_steps(3);
+    assert!(h.state().backstage.is_none(), "and closes when the host turns the File tab off");
+}