Hi, I think you’ve made it to the wrong sub (since you’re not looking to self host at all). non the less, here are some pointers. a domain is what you need. it does not matter what you will use it for and how many email addresses you tie to it. get your domain name from a provider with a good dns management tool (personally use cloudflare, but did not buy the domains from cloudflare). domain forwarding to shopify is easy to do. setting up mail with gmail as well. I forgot if they charge though. you can create as many emailaddresses youwant as long as you have ownership of the domain.
Depending on the top level domain designation (.com, .cz, .bet, …) 24 dollars a year can be cheap or expensive. look around.
I run a few dedicated mail servers at hetzner, never had this issue, even from the get go.