I rent a couple of bare-metal servers from Hetzner, and I have physical servers at home.
On my home hardware I keep things like multiple copies of my photos and documents, as well as experimenting a bit with open LLMs etc.
On the rented servers, I host websites, PeerTube, Forgejo, and keep copies of some data I downloaded from elsewhere.
I’ve also previously hosted email on rented servers. Both on rented hardware and on rented VPSes. For the past few years I haven’t bothered with hosting email myself. I use iCloud provided email instead.
Sometimes I upload videos to my PeerTube instance. Sometimes I upload videos to TikTok.
I don’t have some grand vision of self-hosting everything at home. It is impractical, and comes with its own set of drawbacks. Things that only serve myself and my family go on my hardware at home. Things that I want others to be able to reach go on the rented servers. And other times like with email and TikTok I use services where I have no control whatsoever over what the service provider does with my data.
If someone decides that a particular service is neat to host on rented servers I won’t fault them for it. And I consider things that you manage on your own to be self-hosted even if you don’t own the hardware it’s running on.
You decided to rent a $5 VPS for your email? You’ll still learn things from that even if the server is not in your home. And I will perfectly agree that it fits the name self-hosted email. Same goes for anything else you set up and manage, regardless of whether it’s running on bare metal or in a VPS, and regardless of whether the computer it runs on is in your home or rented from someone else.