CyborgManatee's post in Web Client Keeps Asking Me to Choose Subscription was marked as the answer
I said I knew for a fact because I had already checked those settings. There were two devices registered (an older PC and my current one) and I removed both before signing in again. But it turns out what I was seeing was just an ad for a lower price with a hard to notice way to cancel out of it. Kind of annoying that it's designed that way, but at least I figured it out.