This is like saying you're self-hosting a game server because it's not hosted on the developers' server, but on the server of some other random third party you're paying to run it. No, self-hosting means you run it on hardware you own. Cloudflare is no stranger to redefining completely established terms for marketing reasons (see 'Cloudflare OS'), how about we stop buying it every time?
So like, running bitwarden on a VPS counts as self-hosting even if the VPS isn't physically in your home.
And installing postgres or redis on the VPS counts as self-hosting as opposed to paying for a dedicated database.
So does installing your own web server. Running your own ACME client for certificates. Etc.
It doesn't require hardware you own, the idea of self-hosting includes software you control.