In Mastodon/Lemmy/Kbin/ActivityPub, your identity is tied to your instance. So if your instance shuts down, you lose all your followers/followees/subscriptions/DMs
In Nostr, your identity is your public key so your relay can shut down and everything is fine since your identity isn’t tied to your relay/instance.
BlueSky’s proposed solution to this is to have your username be yourname@somedomainyouown.com. Which requires buying a domain name, which are limited resources, costs >$10 per year, and requires manually configuring DNS records which is not fun.
Background:
Will it work on a subdomain of something I already own
I believe so, yes.