I think almost any judge or jury would find it implausible if you told them you thought the written ban didn't apply anymore because the server still let you into the coffee shop. We intuitively understand that written notice from a property owner carriers more weight than the actions of one of their workers. I think the same exact reasoning applies where the "worker" is a computer server.

I agree with you, but I think an even better analogy would be a supermarket with automatic doors.

If someone was walked out of a supermarket and explicitly told that they were banned for life, and they tried to claim that the ban was lifted because the automatic doors opened for them, they'd be laughed out of court.

You could extend that further and say that the supermarket has a self-checkout. You may very well be able to walk through the automatic doors, grab something off the shelf, check it out yourself, and leave without anyone noticing you, but it's still trespassing if you've been banned from the store.

I actually think it would be a violation. There is a clear delineation between the private space of the coffee shop and the public space.

It becomes less clear where that delineation is not clear: a menu posted on a window or an automated phone system. These are both private things intended for at-large public consumption. My impression is that the EFF and hiq labs is taking the stance that it's a menu placed in the window, not being let in after being told you can't come in.