feat(app): provider system overhaul with model selector, diagnostics, and UX polish

- Add CombinedModelSelector with two-level drill-down (providers → models),
  favorites section, search, and single-provider auto-drill mode
- Add provider snapshot system (ProviderSnapshotManager) for cached provider/model state
- Add provider diagnostics with resolved binary paths and versions across all providers
- Add StatusBadge shared component for consistent status visual language
- Add ProviderDiagnosticSheet for detailed provider health inspection
- Add desktop auto-focus on input after any status bar interaction (model, mode,
  thinking, features) using focusWithRetries
- Fix Combobox flicker on height change by switching to bottom-based CSS positioning
  once initial floating-ui position resolves
- Add dynamic dropdown height: Level 1 fits content, Level 2 calculates from model count
- Remove "Other providers" section from model selector (only show available providers)

packages/app/src/components/agent-input-area.tsx

@@ -213,7 +213,13 @@ export function AgentInputArea({
 
   const focusInput = useCallback(() => {
     if (Platform.OS !== "web") return;
-    messageInputRef.current?.focus();
+    focusWithRetries({
+      focus: () => messageInputRef.current?.focus(),
+      isFocused: () => {
+        const el = messageInputRef.current?.getNativeElement?.() ?? null;
+        return el != null && document.activeElement === el;
+      },
+    });
   }, []);
 
   useEffect(() => {