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/server.ts

@@ -93,7 +93,7 @@ export function start(
           res.writeHead(500, { Connection: "close" });
           res.end(`${err.name}: ${err.message}`);
         }
-      } catch (err) {
+      } catch {
         // Ignore
       }
       throw err;