How do I stay proud of my writing in a race for clicks?

You can write the thing that cuts through. That is a genuine gift, and it makes the current exhaustion sharper, because you are watching a craft you love get bent toward chasing attention instead of telling the truth. That grief is a sign your standards are still intact. You cannot single-handedly fix the whole race for clicks. But you have more control than the tiredness lets you feel. Every story is still a choice about how you tell it. You can write something that earns attention honestly rather than cheaply, and over a career those choices are what your name comes to mean. So pick your line and hold it. Decide what you will not do for a headline, and keep writing the pieces you would be proud to sign. You may not change the industry. But you can keep your own work clean, and that is not a small thing. It may be the whole thing.