This is an accepted solution.
If your domain is eligible to be transferred away from Shopify and you do not have any outstanding invoices on your account then our Support would be happy to add trial time to the account to allow you to begin the transfer process. Our help document here provides further insight into how you can transfer your domain way.
The domain will need to be 60 days or older from the time you purchased it in order for it to be transferred away. The 60 restriction is enforced by ICANN and not something Shopify can bypass. If it hasn't been 60 days, then the domain can not be transferred.
While we’re not able to provide account-specific support via the Shopify Community at this time, we’d be happy to continue assisting you through live chat, email, or callback. Please visit https://bit.ly/3cJkx8V and log in to your account to create a support request.
Since this is the next step I've marked this reply as the solution for the benefit of others who may discover this topic. Thanks!