Add browser storage fallback for Firefox/Safari (#1)

IndexedDB-based storage backend with Storage Persistence API for browsers
without File System Access API support. Requests persistent storage on
first save to protect data from automatic eviction. Includes backup
rotation (last 10 saves) and appropriate UI banner.

web/app.jsx

@@ -87,6 +87,12 @@ function App() {
 
         if (mode === 'local') { setIsLoading(false); return; }
 
+        if (mode === 'browser') {
+          if (cancelled) return;
+          await applyStorageData(mode, () => cancelled);
+          return;
+        }
+
         if (mode === 'direct') {
           // Try silent reconnect — works if permission is still active from a previous session.
           const ok = await Storage.tryAutoConnect();
@@ -528,6 +534,16 @@ function App() {
         </div>
       )}
 
+      {storageMode === 'browser' && (
+        <div className="banner info" style={{gap:8}}>
+          <Icon name="folder" size={14}/>
+          <span>
+            Data saved in <strong>browser storage</strong> — persists until you clear site data.{' '}
+            Use <em>Import/Export</em> to back up to a file.
+          </span>
+        </div>
+      )}
+
       {needsConnect && (
         <div className="banner info">
           <Icon name="folder" size={14}/>
@@ -758,7 +774,7 @@ function ViewChips({ filters, setFilters }) {
 
 // ----- Header -----
 function Header({ view, setView, saveState, saveLabel, storageMode, searchValue, onSearch, onOpenImportExport }) {
-  const modeIcon = storageMode === 'api' ? '⚡' : storageMode === 'direct' ? '📁' : '💾';
+  const modeIcon = storageMode === 'api' ? '⚡' : storageMode === 'direct' ? '📁' : storageMode === 'browser' ? '🌐' : '💾';
   return (
     <header className="header">
       <div className="brand">