Normally I'd agree that unauthenticated privilege escalation to administrator account is something that should only ever be reported privately, but this sounds more like a caching bug on the sopuli instance, in which case OP didn't actually have (theoretical) access to the cookie, although it may be something else. It also brings to attention the lack of published email and optional PGP for reporting. Though, that it was the admin account makes me wonder if the admin wasn't tinkering with something, causing this to happen for a split second.
@freedomPusher@sopuli.xyz I'm curious to hear the response from the admin, will you ping me if they don't mind you sharing their response?
I didn't notice OP said it changed on the same page load, I thought they were F5ing their comments. That does make it more strange.