The fonts are actually “hidden” inside the executable files for Word, Excel, and PowerPoint and are not visible to other applications, including Adobe Acrobat (or any other Adobe applications).
Whereas installation of Microsoft Office on Windows actually installs the Perpetua font family in the Windows Fonts directory, under MacOS, Microsoft Office does not install the Perpetua font family in such a way that it is available to applications other than the MacOS Microsoft Office applications themselves. The key to this is that you can see the Perpetua font in the font drop-down list in Microsoft Word and that you are running Microsoft Office on MacOS. The answer to this question turns out to be fairly simple, I'm afraid.