How differential pairs should be called out on fabrication print?
You can do that, or you can call the diff pairs out as width and spacing.  Really however you communicate well with your shop is fine.   Even better if you call them at the start of your design to work on the stackup with them. Nobody knows their process like they do.   It could be easier/cheaper for you to make a minor change that you wouldn't know about otherwise.

Also I'd say you should be specing your dielectric thicknesses and your over all board thickness. The shop will likely slightly adjust your widths based on what they know about their etching and lamination process.

That's another part of the Stackup that is nice to work with your shop on ahead of time.