I am seeing the same issue after upgrading to Skim 1.6.1 on Big Sur - downgrading back to Skim 1.5.13 and relaunching the Finder replaces the PDF file icons.
I am seeing the same issue after upgrading to Skim 1.16.1 on Big Sur - downgrading back to Skim 1.5.13 and relaunching the Finder replaces the PDF file icons.
I am seeing the same issue after upgrading to Skim 1.16.1 on Big Sur - downgrading back to Skim 1.15.13 and relaunching the Finder replaces the PDF file icons.
I see the current theory is this is a SourceForge problem, just wanted to chime in that I've been having the exact same issue for a few months and have been downloading the update dmg's directly as a workaround.