There is a webmaster, you can contact them. Senators have no direct control over websites like this, and are unlikely to have the faintest clue what to do about this.
I'm not sure if they would even know what "website vulnerabilities" are.
You are correct. It is better to email their customer support or webmaster if available. Still, many websites have horrible reporting features and even worse response rates.
I'm not sure if they would even know what "website vulnerabilities" are.