It's not specifically enshrined because it doesn't need to be. It's implied under the bill of rights: "no state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law ... nor deny any person the equal protection of the laws," (Amendment 14 Section 1).
Again, then it is a worthwhile argument to ask why certain things are enshrined when others are not, if it is indeed possible to base a legal system upon what reasonable minds agree is "implied". For example, most people today would agree that not enslaving humans is implied under the equal protection clause., and yet, we have a specific amendment that had to be ratified, stating "No person can hold another as a slave..."
Like most implied rights, the right to privacy is weak specifically because it is not enshrined. Even the explicitly stated rights have limits, particularly when they butt into the other explicitly stated rights.
When the implied "right to privacy" butts into the 1st Amendment rights of freedom of expression and a free press, on which side do you think the courts will err on, on a consistent basis?
But salaries are not really private. The company has salaries. The state often makes their salaries public.
The IRS has that information. Credit agencies do, etc.
The state has gained an absolute right to know your wage, which one could argue that abolishes the private nature of that information, much like your gender, or your face.
https://en.wikipedia.org/wiki/Griswold_v._Connecticut