You can transfer a domain, but I afaik they don't take offer web/mail hosting for domains registered elsewhere at all. It's not totally ideal if you want to decouple your domain registration from your mail hosting.
Also, can't recommend paying 25% more to be billed in USD instead of EUR.
Appears you'd need to go for the $6/m tier + extra fee to use an existing domain that's registered elsewhere? https://www.hetzner.com/webhosting/matrix-mobile/