How do I search PDFs in Acrobat in Safari using command-f, without an extra buttom press?
You are oping the PDF files using the Safari PDF reader. 

You need the AdobePDFViewer.plugin to replace the Safari build in PDF reader. 

Here are the instructions how to do that.



Update:

Based on our discussion and your very specific needs here is a proposal.

Reassign the Safari default for "Find" keyboard short cut.

Open sys pref- keyboard - shortcuts.

Click on app shortcut

Select Safari

Type "Find..." (the 3 dots are important)

Select new short cut "shift + cmd + F"

Now when you use the "cmd -F" only Adobe search will show

When you use the shift- cmd -F the Safari search will show up.