feat(ui): render the map source chips and status badge from the store

createMapSourceControls() (./ui/maps) no longer builds the chip row or
writes the status badge: it presents both and hands them to its publish
option, so the entry stays Vue-free. The shell publishes them to the
gev-display store and connects the controls, and the dock renders the
chips and calls select() for an available one. renderMapStackChips and
syncMapStackChips are deprecated. The map source QA harnesses wait for
the dock to render and no longer read the removed element refs.

scripts/qa-map-source-controls.mjs

@@ -69,9 +69,10 @@ try {
     await page.evaluate(() => {
       const manager = window.__godsEyeView.styleManager;
       return (
-        manager._mapStackChips.querySelector('[aria-pressed="true"]')?.dataset
-          .stackId === 'osm' &&
-        manager._mapStackStatus.textContent ===
+        document
+          .getElementById('map-stack-chips')
+          .querySelector('[aria-pressed="true"]')?.dataset.stackId === 'osm' &&
+        document.getElementById('map-stack-status').textContent ===
           manager.mapStackController.getState().activeStack.shortLabel
       );
     }),
@@ -81,32 +82,38 @@ try {
     await page.evaluate(async () => {
       const manager = window.__godsEyeView.styleManager;
       const result = await manager.setMapStack('esri-imagery');
+      // The dock renders the published row on Vue's next flush.
+      await new Promise((resolve) => setTimeout(resolve, 0));
       const active = manager.mapStackController.getActiveId();
       return (
         window.__qaMapSelections.at(-1) === 'esri-imagery' &&
-        manager._mapStackChips.querySelector('[aria-pressed="true"]')?.dataset
-          .stackId === active &&
+        document
+          .getElementById('map-stack-chips')
+          .querySelector('[aria-pressed="true"]')?.dataset.stackId === active &&
         (result.ok || !!manager.mapStackController.getState().lastError)
       );
     }),
   );
   check(
-    'refresh revokes retained old chips',
-    await page.evaluate(() => {
+    'refresh re-presents the chips without duplicating them',
+    await page.evaluate(async () => {
       const manager = window.__godsEyeView.styleManager;
-      const old = manager._mapStackChips.querySelector('[data-stack-id="osm"]');
       manager._mapSourceControls.refresh();
-      const before = window.__qaMapSelections.length;
-      old.click();
-      return window.__qaMapSelections.length === before;
+      await new Promise((resolve) => setTimeout(resolve, 0));
+      return (
+        document.querySelectorAll('#map-stack-chips [data-stack-id="osm"]')
+          .length === 1
+      );
     }),
   );
   check(
     'refreshed chips still select once',
     await page.evaluate(async () => {
-      const manager = window.__godsEyeView.styleManager;
       const before = window.__qaMapSelections.length;
-      manager._mapStackChips.querySelector('[data-stack-id="osm"]').click();
+      document
+        .getElementById('map-stack-chips')
+        .querySelector('[data-stack-id="osm"]')
+        .click();
       await Promise.resolve();
       return window.__qaMapSelections.length === before + 1;
     }),
@@ -188,7 +195,10 @@ try {
       const manager = window.__godsEyeView.styleManager;
       const before = window.__qaMapSelections.length;
       manager._mapSourceControls.destroy();
-      manager._mapStackChips.querySelector('[data-stack-id="osm"]').click();
+      document
+        .getElementById('map-stack-chips')
+        .querySelector('[data-stack-id="osm"]')
+        .click();
       const result = await manager._mapSourceControls.select('esri-imagery');
       return result === null && window.__qaMapSelections.length === before;
     }),

scripts/qa-map-source-tray.mjs

@@ -871,6 +871,9 @@ try {
       return originalSetStack(stackId);
     };
     const switchPromise = styleManager._setMapStack('osm', { syncShare: false });
+    // The dock renders the published row on Vue's next flush.
+    const rendered = () => new Promise((resolve) => setTimeout(resolve, 0));
+    await rendered();
     const during = {
       status: document.getElementById('map-stack-status').textContent,
       active: [...document.querySelectorAll('.map-stack-chip')]
@@ -879,6 +882,7 @@ try {
     };
     release();
     await switchPromise;
+    await rendered();
     const after = {
       status: document.getElementById('map-stack-status').textContent,
       active: [...document.querySelectorAll('.map-stack-chip')]