I was thinking about how to improve my email situation, because at the moment I am using an address of a commercial mail provider, which obviously brings some concerns of lock-in.

While fully self-hosting the email is an option, I am a bit wary of this, because having a working email is very critical and I do trust the commercial providers to give better uptime and reliability than my old server in the closet. Does anyone have experience hosting an email service and what is it like/could you recommend it?

The other option that I am more inclined to is having the email hosted by some cloud provider, but using an address under my personal domain name. The point would be of course that I could change the email provider while keeping the address. Which providers supporting this could you recommend? What is the process like linking a domain to an email host?