If you want to build something on land that could be rendered useless by the actions of the owner of adjacent land, you buy an easement.
If you can't reach an agreement on a price for that easement, you either don't build, or you assume the risk.
This isn't rocket science, except to those who think that they have a right to things they haven't earned or paid for.
This is government vs. government. None of that ownership stuff counts!
The library should make a quick alliance with the National Guard and simply make war on the city.
Then again, this is a parking garage going up in a part of the world that still has plenty of unused sidewalks to use! (ommon in Europe).
Don't these people have something better to do?