feat: add default Authorization Bearer header and clean up legacy auth

- Provide "Authorization: Bearer " as default starting header
- Remove legacy auth props from components
- Centralize migration logic and fix localStorage cleanup
- Update tests for new auth architecture

client/eslint.config.js

@@ -23,10 +23,6 @@ export default tseslint.config(
         "warn",
         { allowConstantExport: true },
       ],
-      "@typescript-eslint/no-unused-vars": [
-        "error",
-        { argsIgnorePattern: "^_" },
-      ],
     },
   },
 );