It takes a particular kind of nerve to end a psalm this way. David has just spent twenty-two verses describing how completely God knows him — his sitting down and rising up, his thoughts from far off, his words before they are spoken, his body before it was formed. Having established that there is nowhere to hide, he asks God to look harder.
Search me, O God, and know my heart: try me, and know my thoughts. This is not a request for information God lacks. It is a request to be shown what God already sees and David does not. That is the honest admission underneath the prayer: I am not a reliable witness about myself.
We all run a version of ourselves in our own heads that is flattering in the places it needs to be. We know our motives were mixed and we describe them as pure. We know why we said that and we tell ourselves a kinder story. The psalm asks for that gap to be closed — see if there be any wicked way in me.
But look at how it ends: lead me in the way everlasting. The point of the searching is not exposure for its own sake. It is direction. He asks to be examined by someone he trusts to do something good with what is found.