Sorry for my late response. Life got in the way. 
I’m indeed using a mail client; just Apple Mail for now. AFAIK, Apple Mail stores all its data inside the Library folder. So if I’m backing up my home folder (which encloses the Library folder), I should be safe?
It would be ok, if I would only be able to open the backed up emails on another Mac again. However, I would prefer some kind of “open” format for future-proofing things. I will look into the EML format. As far as I understand, though, this only relates to separate emails. I, however, would like to export the mailbox (= my account) as a whole.