> but (1) I’m referring to a registrar/issuer, which makes it yet more complicated
We're also talking about a ccTLD which makes it even more complicated. AFAIK those fall entirely under the jurisdiction of the respective UN recognized government although I don't know how strong that agreement is in practice (treaty versus something else).
So at that point I guess we've roughly got ICANN -> US federal government -> CA state government -> registrar -> private party -> sublet.
This isn’t how things are done these days; names visible to the public are pretty much always in the form {domain}.{tld} or sometimes {name}.{domain}.{tld} (e.g. my own https://samboy.github.io). Registration is now done by bots and companies that spam you to death to try and get more money from you (the Internet wasn’t like that in the beach.santa-cruz.ca.us days). Domain names with multiple levels of delegation aren’t around they way they used to be.
* rented/leased/had control over/whatever
The old locality domains still exist, and in many localities you can still register them today by the same "email a request to some sysadmin" process. https://news.ycombinator.com/item?id=48122635
Your beach.santa-cruz.ca.us domain is still in DNS, just with a broken delegation chain. You could reclaim it right now by setting up a nameserver at reality.samiam.org.
https://beach.santa-cruz.ca.us/
Thanks for checking the zone files of the parent domain to verify it’s still there.