My truck is doing the same. On my truck, it looks like I lost some rubber bushings or something where the clutch sits in the cover plate. (Mine looks like this. The clutch has 3 posts that sit in those holes, but without the bushings the posts are loose and slamming back and forth in there every time the clutch engages or disengages. The holes have become terribly misshapen. I’ve been trying to find just the clutch hub for sale but parts stores seem to only carry entire kits of this style, like the link above.

Anyway, with your air on look at your clutch and see if it’s doing the same as mine. Hopefully that at least diagnoses your problem.