How do I hold onto my ideals working in government?

You came in to serve the public good, and the slow grind of bureaucracy is wearing the idealism right off you. That ache is what happens when someone who genuinely cares meets a system that moves at the speed of stone. It does not mean your ideals were naive. It means they are colliding with reality, and that collision is exhausting. Change in the public world is slow, and slow is not the same as never. The idealists who last are the ones who trade the dream of fast, sweeping wins for the reality of small, durable ones. A single rule made a little fairer, one process that helps real people a bit more, that is the actual shape of public good. It is less thrilling and more real. Find the piece of your work where you can see an actual person helped, and let that be your fuel instead of the big vision that keeps getting stuck. Protect your idealism by aiming it at something small enough to move. Burnout comes from pushing on the immovable. Meaning comes from moving what you actually can.