Skim is a great app, but it has one significant limitation. Search doesn't support wildcards or booleans. You can search for a word or a phrase. That's it. If you need to find a page where two words appear separately, then you are out of luck
The other day I needed to find the title capitalization rules for infinitives. I needed pages that used the words capital, capitals, capitalize or capitalization. And the word "infinitive" also needed to appear anywhere on those pages.
In Skim, you can find where any form of "capital" appears. If you type "capital", it will show pages that contain capital, capitals, capitalize, and capitalization. However, as soon as you hit the space bar, you are locked into a search for the exact word you typed. Any search for two or more words will be an exact phrase search.
You can find where "infinitive" appears. But there is no way to find where it appears anywhere on the same page with some form of "capital". The exact phrases "capital infinitive", "infinitive capital", "infinitive capitalization", "capitalize infinitive", etc. produce zero search results And that exhausts the Skim search capabilities.
I opened the document in Preview and searched for "capital* AND infinitive". It immediately found the exact page I needed--where the words "capitalization" and "infinitive" appeared in different parts of the page, about three sentences apart.
I searched Skim's "Issues" page on GitHub and found that someone had brought this to the developer's attention a few years ago. The developer said Skim was using the search capabilities provided by Apple's PDFKit so if you want improved search, then you should talk to Apple. He then marked the issue as closed.
In other words, it is unlikely Skim's search capabilities are going to get any better . . . at least not anytime soon.
If you need to annotate PDFs, there is nothing better than Skim. If you require anything more than the most basic search functionality, you will need to use a different app.