Does the test email getting sent from the contact form settings?
Would you mind if I log in to your site and do some troubleshooting? If this is ok then could you please temporary share me your site admin login details privately by adding them in the box having text “Enter your private content here (only you and forum moderators will be able see it)”?
I logged into your site and saw you are using custom domain specific email address but not configured the contact form SMTP settings as shown in the attached screenshot so please configure it by contacting your web host.