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/connection-request.ts

@@ -157,7 +157,7 @@ export async function httpConnectionRequest(
         authHeader = auth.parseWwwAuthenticateHeader(
           res.headers["www-authenticate"],
         );
-      } catch (err) {
+      } catch {
         return "Connection request error: Error parsing www-authenticate header";
       }
       [username, password, authExp] = await extractAuth(authExp, false);