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/ui/status-badge.tsx

@@ -0,0 +1,65 @@
+import { View, Text } from "react-native";
+import { StyleSheet, useUnistyles } from "react-native-unistyles";
+
+type StatusBadgeVariant = "success" | "error" | "muted";
+
+interface StatusBadgeProps {
+  label: string;
+  variant?: StatusBadgeVariant;
+}
+
+export function StatusBadge({ label, variant = "muted" }: StatusBadgeProps) {
+  const { theme } = useUnistyles();
+
+  return (
+    <View
+      style={[
+        styles.pill,
+        variant === "success" && styles.pillSuccess,
+        variant === "error" && styles.pillError,
+      ]}
+    >
+      <Text
+        style={[
+          styles.pillText,
+          variant === "success" && styles.pillTextSuccess,
+          variant === "error" && styles.pillTextError,
+        ]}
+      >
+        {label}
+      </Text>
+    </View>
+  );
+}
+
+const styles = StyleSheet.create((theme) => ({
+  pill: {
+    flexDirection: "row",
+    alignItems: "center",
+    borderRadius: theme.borderRadius.full,
+    borderWidth: 1,
+    borderColor: theme.colors.border,
+    backgroundColor: theme.colors.surface3,
+    paddingHorizontal: theme.spacing[2],
+    paddingVertical: 3,
+  },
+  pillSuccess: {
+    backgroundColor: theme.colors.palette.green[900],
+    borderColor: theme.colors.palette.green[800],
+  },
+  pillError: {
+    backgroundColor: theme.colors.palette.red[900],
+    borderColor: theme.colors.palette.red[800],
+  },
+  pillText: {
+    fontSize: theme.fontSize.xs,
+    fontWeight: theme.fontWeight.normal,
+    color: theme.colors.foregroundMuted,
+  },
+  pillTextSuccess: {
+    color: theme.colors.palette.green[400],
+  },
+  pillTextError: {
+    color: theme.colors.palette.red[500],
+  },
+}));