I think I was having the same issue, and what solved it for me was to give Hookmark Full Disk Access. It already had access to my Dropbox folder, and my Documents folder, but it merely opened PDFs, but did not scroll to the page for me, despite the URL seeming to be correct for Hookmark.
After playing around with the URL, changing it to use skim:/// style links (complete with the #page=100 format, rather than “#p=100” as skim uses), and then re-copying the link from Hookmark, it occurred to me that MacOS didn’t give Hookmark the access it needed. With full disk access, Hookmark started taking me to the correct page in Skim.
I didn’t see anyone mention their Mac OS version, so maybe that’s got something to do with it?
Mac OS 13.1, M1 Macbook Pro
Hookmark 4.0.1
Skim 1.6.14