build: migrate eslint to v10 flat config and upgrade typescript

Replace .eslintrc.json with eslint.config.js using the new flat config
format required by ESLint 10. Swap @typescript-eslint/eslint-plugin and
@typescript-eslint/parser for the unified typescript-eslint package.
Upgrade TypeScript to 5.9 and @types/node to 25. Apply automatic code
fixes: remove unused catch bindings and preserve error cause in auth
header parsing.

lib/auth.ts

@@ -25,7 +25,7 @@ function parseHeaderFeilds(str: string): Record<string, string> {
       try {
         value = JSON.parse(value);
       } catch (error) {
-        throw new Error("Unable to parse auth header");
+        throw new Error("Unable to parse auth header", { cause: error });
       }
     }
     res[name.trim()] = value;