Thanks for bringing your question to our Community forum. I understand that you are hoping to access your custom domain settings. I'm more than happy to help!
Based on the screenshot that you've shared, it looks like you've connected a third-party domain (GoDaddy) with your Shopify store. For this reason, you will not see the option to manage your domain within Shopify. To access your DNS records, you will need to do so through your GoDaddy account.
To ensure that I'm on the same page, are you hoping to set up email forwarding or email hosting? Email forwarding is a service that enables you to direct an email message that's sent to one email address to another email address. If you have a Shopify-managed domain, then you can set up an unlimited number of custom domain email addresses that forward to an email account hosted by a third party. However, since you are using a third-party domain then you can't set up email forwarding addresses from your Shopify admin. Email forwarding or hosting might be offered by your third-party domain provider, or you can transfer your domain to Shopify. I recommend reaching out to GoDaddy to inquire about setting up email forwarding for your domain if that is your desired outcome.
Please let me know if you have any questions about that! In the meantime, I'd love to hear more about your business! What kind of products do you sell?
In order to ensure that you receive the help you require, I wanted to check in. If you have any questions, don't hesitate to reach back out!
Thanks for getting back to me. I'm so happy to hear that. All the best with your store!