I'm fascinated by the fact that my takeaway is the precise opposite of what the author intended. To me, the answer to all of the questions was crystal-clear. Yes, you can academically wonder whether an orbiting space station is a vehicle and whether it's in the park, but the obvious intent of the sign couldn't be clearer. Cars/trucks/motorcycles aren't allowed, and obviously police and ambulances (and fire trucks) do…
By "doing their jobs", you presumably mean "responding to an emergency call", right? Because, e.g., cops in normal transit from A to B are "doing their jobs" but letting them drive through a "no vehicles allowed" park in that instance is probably bad. Or if they're on a high-speed chase - definitely "doing their jobs" but not something you'd want to happen through a park.
> an example of how content moderation rules are unclear to follow
You've amply demonstrated this by creating a huge muddy mess around "emergency services doing their jobs".