It does seem like the chat app does actually recognize your elite status now. It responds differently depending on whether you supply a miles number with status or one without. Weird they didn't take a step further and have it call out your specific elite tier, but maybe just a design choice.

Anyway, I can also confirm I got connected to a chat rep very quickly as an elite member. Didn't test without the number to see if they are pushing elites up the queue or not... but in any case, huge improvement. Hope it lasts!