PDF Preview in Mac OS Big Sur

Though gridlines are not a feature inherent to Preview, there is an Automator action named Add Grid to PDF Documents that allows you to apply a customizable grid color and spacing in inches, centimeters, or points either under or over the PDF.

An Automator application would allow you to drop a PDF onto it, apply the grid, and then move the resultant PDF to a designated location.

This Automator workflow created a blue grid of half-inch (36.0 pt) spacing on a blank PDF that was dropped on it.

and the grid on the PDF looks like the following (right-click on ask to display in a new browser window for full size):

If you created the Automator application, as I shared, and saved it on your Desktop, it becomes a drag and drop (PDF) target.

Preview is not a PDF editor, and it can only add selected content from its markup toolbar as an annotation layer.

There is no grid overlay, as I expected that is what you really wanted, and your recourse is to purchase a third-party PDF editor from the Mac App Store (e.g. PDFpen, PDF Expert, etc.) that provides a grid overlay, and the ability to add the content you mentioned.

I might add that Adobe Acrobat Reader DC does not provide a grid or ruler overlay feature, but the subscription Adobe Acrobat Pro does offer it. Similarly, the PDFpenPro 12 Editor also has a switchable Arrange menu Show grid, and snap to grid feature.

You save this Automator application to your Desktop. Then you drag and drop a PDF file on it, and a new PDF file is written on your Desktop with the applied gridlines.