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/contexts/session-context.tsx

@@ -1105,6 +1105,7 @@ function SessionProviderInternal({ children, serverId, client }: SessionProvider
           hostname: serverInfo.hostname,
           version: serverInfo.version,
           ...(serverInfo.capabilities ? { capabilities: serverInfo.capabilities } : {}),
+          ...(serverInfo.features ? { features: serverInfo.features } : {}),
         });
         return;
       }