Add Prettier for TypeScript formatting

- Install prettier
- Configure .prettierrc.json and .prettierignore
- Add npm scripts: format, format:check
- Add Makefile target: format-frontend
- Format all frontend files

frontend/app/auth-context.tsx

@@ -25,7 +25,7 @@ export const Permission = {
   CANCEL_ANY_APPOINTMENT: "cancel_any_appointment",
 } as const;
 
-export type PermissionType = typeof Permission[keyof typeof Permission];
+export type PermissionType = (typeof Permission)[keyof typeof Permission];
 
 // Use generated type from OpenAPI schema
 type User = components["schemas"]["UserResponse"];
@@ -100,13 +100,19 @@ export function AuthProvider({ children }: { children: ReactNode }) {
     setUser(null);
   };
 
-  const hasPermission = useCallback((permission: PermissionType): boolean => {
-    return user?.permissions.includes(permission) ?? false;
-  }, [user]);
+  const hasPermission = useCallback(
+    (permission: PermissionType): boolean => {
+      return user?.permissions.includes(permission) ?? false;
+    },
+    [user]
+  );
 
-  const hasRole = useCallback((role: string): boolean => {
-    return user?.roles.includes(role) ?? false;
-  }, [user]);
+  const hasRole = useCallback(
+    (role: string): boolean => {
+      return user?.roles.includes(role) ?? false;
+    },
+    [user]
+  );
 
   return (
     <AuthContext.Provider