Couldn’t the same analogy be used if I left my front door unlocked? The door would happily say: “yes, you may enter” to anyone trying the handle.

I think the real question here is: did the website provide enough information for the user to have been assumed to understand that what they were accessing wasn’t meant to be public (e.g. did the door look like a door to a private property)? And did the user cease to access the data once they understood it (e.g. did they close the door and leave)?

That analogy would be more accurate if you also operated a cafe out of your living room, with a big "open" sign on the front door, and someone accidentally used your personal bathroom because you failed to stick a "private" sign on it. In that case, it would be unreasonable to sue someone for trespass.

Web servers are not houses. They are implicitly public, whereas houses are implicitly private.

Totally agree with this. If the web resource is available to anyone, then how could you be mad that some one saw it.