fix(todo): the Plan's button before search, and its sheet without the navigation bar

Today's and Upcoming's Plan button stood between search and Display; it
stands before the three every tab has now (TabScreen's `leadingActions`).
On a phone, where the Plan opens over the hours' foot, its icon is
Lucide's panel-bottom-open (panel-bottom-close while open); beside the
hours on wider windows it keeps the panel at the right.

While a phone's Plan is open, the navigation bar steps aside, as it does
while tasks are being chosen: it floated over the Plan's tasks, and the
Plan can't be a modal sheet, its rows being dragged out onto the hours.
`NavigationBarHold`, kept by TodoShell, holds it away while anyone asks;
closing the Plan, or back, which closes it first, brings it back.

The Plan's heading put its projects and close button after a spacer of
one share and a flexible of four, leaving a fifth of the room after
them; they end at its edge now, as the rest of it.

Whats-New: The Plan's button stands before search, and while the Plan is open the navigation bar makes way for it.
Whats-New-De: Der Plan-Knopf steht vor der Suche, und solange der Plan offen ist, macht ihm die Navigationsleiste Platz.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Signed-off-by: Tizian 「ティツィアーン」 <raisondetredev@pm.me>

apps/todo/halkyon_todo_flutter/test/app/todo_app_test.dart

@@ -1963,6 +1963,12 @@ void main() {
         expect(find.byKey(UpcomingTab.planKey), findsNothing);
         await threeDay(tester);
         expect(find.byKey(UpcomingTab.planKey), findsOneWidget);
+        // Before search, Display and the menu every tab has (the
+        // developer's review, 7 Nov 2026).
+        expect(
+          tester.getTopRight(find.byKey(UpcomingTab.planKey)).dx,
+          lessThanOrEqualTo(tester.getTopLeft(find.byTooltip('Search')).dx),
+        );
         tester.view.physicalSize = const Size(1400, 900);
         await tester.pumpAndSettle();
         expect(find.text('No date'), findsOneWidget);
@@ -2690,6 +2696,76 @@ void main() {
         });
       });
 
+      testWidgets('on a phone, Plan stands before search, pointing down where '
+          'it opens; open, the navigation bar steps aside until it is '
+          'closed or back is pressed, its projects and close button at its '
+          "end (the developer's review, 7 Nov 2026)", (tester) async {
+        await start(tester, usedBefore: true);
+        // A wide phone, room to spare beside the heading's projects.
+        tester.view.physicalSize = const Size(560, 900);
+        await calendar(tester);
+        final plan = find.byKey(TodayTab.planKey);
+        final search = tester.getTopLeft(find.byTooltip('Search')).dx;
+        expect(tester.getTopRight(plan).dx, lessThanOrEqualTo(search));
+        expect(
+          search,
+          lessThan(tester.getTopLeft(find.byTooltip('Display')).dx),
+        );
+        expect(
+          find.descendant(
+            of: plan,
+            matching: find.byIcon(LucideIcons.panelBottomOpen),
+          ),
+          findsOneWidget,
+        );
+        expect(find.byType(NavigationBar), findsOneWidget);
+
+        await tester.tap(plan);
+        await tester.pumpAndSettle();
+        final sheet = find.byKey(TodayTab.planSheetKey);
+        expect(sheet, findsOneWidget);
+        expect(find.byType(NavigationBar), findsNothing);
+        expect(
+          find.descendant(
+            of: plan,
+            matching: find.byIcon(LucideIcons.panelBottomClose),
+          ),
+          findsOneWidget,
+        );
+        expect(
+          tester.getBottomLeft(sheet).dy,
+          900,
+          reason: 'down to the foot, no bar below it',
+        );
+
+        final close = find.ancestor(
+          of: find.descendant(
+            of: sheet,
+            matching: find.byTooltip('Hide the Plan'),
+          ),
+          matching: find.byType(IconButton),
+        );
+        expect(tester.getTopRight(close).dx, tester.getTopRight(sheet).dx - 4);
+        expect(
+          tester.getTopRight(find.byKey(PlanPanel.projectsKey)).dx,
+          moreOrLessEquals(tester.getTopLeft(close).dx, epsilon: 1),
+        );
+
+        await tester.tap(close);
+        await tester.pumpAndSettle();
+        expect(sheet, findsNothing);
+        expect(find.byType(NavigationBar), findsOneWidget);
+
+        await tester.tap(plan);
+        await tester.pumpAndSettle();
+        expect(find.byType(NavigationBar), findsNothing);
+        await tester.binding.handlePopRoute();
+        await tester.pumpAndSettle();
+        expect(sheet, findsNothing);
+        expect(find.byType(NavigationBar), findsOneWidget);
+        expect(find.byKey(TodayTab.planKey), findsOneWidget, reason: 'stays');
+      });
+
       testWidgets('on a phone, Plan opens a sheet over the day; a row held '
           'there lowers it out of the way and dropped on 14:00 is planned '
           'then', (tester) async {