I can randomly choose any PDF on Monterey 12.1 and open it in Preview. Doesn't matter if it was produced by Pages v11.2, or Pages 5.6, or any number of other PDF generation tools.
The Finder can hide (but not remove) the PDF extension and Preview will still open the PDF because the extension (even though its display is hidden) is still on it, and the operating system understands that it is truly a PDF document.
Pages v11.2 on Monterey 12.1 appends the .pdf extension to documents exported as PDF, or as Print > PDF > Save as PDF. The operating system knows these are PDF, and so does Preview. The latter will also open Pages (.pages) documents. Much older versions of Pages used to export as PDF with a hidden .pdf extension, but they were still known to the operating system and Preview as PDF documents and opened appropriately.
If you literally strip the .pdf extension from the file, then the operating system doesn't know what it is, the default opening application becomes TextEdit (displays gibberish), and it can only be forced open in Preview from either the Other category in the Open With sub-menu by deliberately selecting Preview from the Applications folder, or in the Terminal as follows for the file foo:
open -a Preview foo
Never manually remove filename extensions.
