Very interesting. So how do you distinguish between the state and a branch or arm or subsidiary of a state? A department (say, the Department of Motor Vehicles) is clearly the state. What if a public university is operated just like a department? If it's taxpayer-funded, professors are public employees, and management is appointed by the governor?
I could see how it would not be the state if it were separately incorporated, funded, and governed, just like a municipality.
So what's the rule that distinguishes entities that have sovereign immunity from those that don't?
The necessity of the taking for the purpose of operation. Same rule that limits federal government agencies from taking anything they want. A constitutional grant.
Use of this specific photograph is not required by any means that could be seriously construed.
It answers the question of when state sovereignty protects state activities from federal regulation. Questions of when a person can directly sue a state or state entity under federal law and what types of remedies might be available are different, but I'm pretty sure you can find your way to cases that explain those in Garcia's citations (the actual case, if not from the Wikipedia article). I can't remember any good ones off-hand, and sadly I can't articulate a way to frame the issues that would help finding them.
TL;DR: if an individual employee can sue a state transit agency to enforce federal minimum wage, then I can't imagine of any reason sovereign immunity would categorically prohibit enforcing copyright against a public university, especially considering that regulation of copyright is one of the few enumerated powers of the Federal government.
I could see how it would not be the state if it were separately incorporated, funded, and governed, just like a municipality.
So what's the rule that distinguishes entities that have sovereign immunity from those that don't?