Presumably you are referring to the federal government. Which part? For career civil service positions, the fact that you have a university degree matters in determining eligibility and salary. I doubt that where you got it matters much at all. There are hundreds of thousands of these positions. For Foreign Service positions, eligibility starts with an examination. Where you got your college degree does not affect your eligibility to take the exam. You don’t get extra credit added to the score for having attended a prestigious college.
Political appointments may be a different story. Congressional staff jobs may be a different story. But by the time one is eligible for most of these positions, chances are, one has racked up other credentials in addition to a college degree. So it would be hard to tease out just how much the undergraduate name matters in hiring/appointment decisions.
I’ve seen one study (much criticized on CC) that does attribute a significant, measurable earnings difference to the college degree status … when the prestige difference is *very large/i.