Is a master's degree that has been obtained considered invalid, and is repentance sufficient, or must the falsification of employment-related data be reported, given that the purpose of study was to seek knowledge?

What you did by circumventing the college and workplace conditions, and concealing the fact that you were employed to obtain a scholarship, is not permissible because it involves lying and deception. You must repent to Allah Almighty and return the money you unlawfully took to the relevant party in cash, or seek their absolution, without necessarily having to inform them of the full truth. If returning the money is difficult, or if you know it will not be used appropriately, then spend it on general Muslim welfare projects. You could also buy books that college students would benefit from. You must also rectify your academic and employment status to comply with the established conditions.