Elias here with Shopify Support. Thank you for reaching out.
I understand you've bought a new domain and you weren't able to receive the domain verification email. Since the verification email banner has disappeared and the email on file may also need to be adjusted, then we’ll need to access your account in order to resolve this issue. While we’re not able to provide account-specific support via the Shopify Community at this time, our Support team would be happy to continue assisting you through live chat, email, or callback. Please visit the Shopify Help Center and log in to your account to create a support request.
Would you be able to check your domain's DNS settings for any typos in your email? This may help speed up the troubleshooting when contacting our Support team.
Thank you for following up!
To access the domain settings, simply head over to the 'Online store > Domains' and click the manage button beside your purchased domain. After that, look to the right and you can review or edit your email address in the registrar information section.
If you run into any issues with this, our Support team would be able to assist you with this as well. Simply follow the instructions provided from my earlier response, and our Support team can help you sort out the domain issues.
I'd love to know if our Support can resolve this issue for you. Keep me posted!