By definition an email server is not under your control, so the question of whether or not it runs FOSS is a bit moot and in any case impossible to verify.
In terms of privacy-respecting email hosting, Proton, Posteo, and Mailbox all spring to mind.
Exactly this. Services and software are not the same thing, you're asking for a service recommendation and it can't be open-source software because it's not software.
I've enjoyed using proton for my own domain. Adding another 2-3 domains and a second user raises the cost to the point that I just can't justify. ~$200 up front for two years.
It’s not completely FOSS, but I run Port87, which is quite a bit FOSS. It uses Haraka as its SMTP server, SvelteKit as its server framework, Nymph.js as its database layer, Svelte as its frontend framework, and Svelte Material UI as its UI framework.