The noncompete thing is actually a much, much bigger deal than the pay transparency thing. I have a friend who is waiting out a 2Y noncompete that he foolishly agreed to in Texas.
I sort of doubt that's how it works in Texas, but in Germany that's the law! A company can only prevent you from working for a competitor by A) keeping you employed by them; or, B) paying what the competitor would pay you.
When I was an employee in Germany I always thought it would be fun to get stuck in B) and get an "offer" for like 5x my current salary and see what happens.
I don't know anything about Texas non-compete law, but "right to work state" refers to restrictions on unionizing. It has nothing to do with non-compete clauses.
The "right to work" is about restrictions on making unions mandatory, so you are correct but glossing over an important details. In practice it generally means that forming an effective union is much harder and thus harms workers, but theoretically it could be paired with other laws that supported unions but that didn't centralizing their power and removing worker choice.