Yes? Using records such as paystubs, W-2, or 1099.

Obviously, they can be falsified, but I presume we are not talking about that. There is also the Norway method of having the government provide it.

If the idea is for the entire labor market to change significantly due to everyone voluntarily sharing their salary, then we ought to be talking about a mechanism of ensuring honesty, just like an auction (generally) wants to design their auction in such a way that people are honest about their willingness to pay.

Ideally, but you do not need the entire labor market to participate to do it. I am guessing even shining a light on a small, representative set of real time data will be enough to get things moving.