The US government and, indeed, almost every government on earth, scans our atmosphere constantly for alien craft both from earth and using satellites (which is to say, they're looking for missiles and bombers) because it's sort of a core function of national security to control your own airspace. I'm not sure you need anything extra to find "non-human" spacecraft.

And do they systematically release that data for academic researchers to analyze? Or is it automatically classified? If it is classified (hint:it is) then how do we know what they have found?

If you were part of the military brass and your mission was thus the defense of your nation, what would you do if you received radar reports of objects behaving unlike anything else that your known technology could do? And if upon further research your experts determined beyond reasonable doubt that these anomalies are real craft, what would you do? Remember that your mission is to provide every possible military advantage to your country and to prevent other countries from gaining an advantage agsinst you.

Me? I would try to shoot them down to study them and keep the lid on the whole thing to prevent our adversaries from leapfrogging our current technology.

If you have a more detailed criticism I would be happy to address it.

My counterargument is that if the military detected UAPs then they would have both a strong incentive not to inform the public and the means to keep it secret.

Happy to address any other misunderstandings.