I couldn't tell whether the site is a live play or a correspondence site, nor whether chess960 is on offer as an option; I'll find out as soon as I can.
HarryO replied in a comment,
The site used to be called E-Chess960.com. The new site ChessRex still supports Chess960 it's a name change plus a revamp. [...] I think you were already a member of E-Chess960.com and so you should still be a member of ChessRex.
I tried my username for E-Chess960 and discovered that indeed it worked on ChessRex. Right on all counts, Harry, thanks very much!
While I was updating the sidebar ('Correspondence Chess960') to note the change, I added another site that came to my attention recently: RemoteSchach.de, 'Fernschach vom Feinsten im Internet bei RemoteSchach' ('Correspondence Chess on the Internet at its best with RemoteSchach'). The site calls the game 'Schach960'. A few years ago I did a web search on that term and noted that there were less than 2.000 hits. Now I get more than 50.000. Looks like I need to investigate that resource as well as other language variants of 'chess960'.