[Beijinger]

Yes. I have domains with internet.bs and buy email hosting separete from https://www.infomaniak.com/en

Just put your domain name for registration. It will say it is registered already but then offers you the option to buy email hosting. I think it is 18 Euros for 5 Email accounts per year. It is based in Switzerland.

Australian fastmail may be better - I don't have experience myself - but it starts at 60 dollars a year. Maybe someone who is a user can give feedback here.

Regarding infomaniak: They offer a free email service (without your own domain). Maybe you try it out to get a feel if this is right for you and your domain: https://www.infomaniak.com/en/free-email

And hands off to apps that have a registration code. E.g. pleco. They are not linked to your email and you don't lose them if your gmail is gone...

[Beijinger]

Or cheapest solution: internet.bs has email forwarding for free, like many other registrars. You could use it only for service registration and not for emailing. But sometimes companies insist you email them with the registered email and you won't be able to do this then.