I have used diet:kosher and seen other use that tag but there isn’t a wiki page about it, is it OK to use it or is there another way to tag a kosher restaurant?
There is no standard tag. Looking at Taginfo, it seems diet:kosher is the most used in practice. So I would advice using AND documenting it by creating that missing Wiki page.
In general, anyone may create and document new tags (as long as they’re not redefining existing widely used tags). See this for an example of a “young” tag: https://wiki.openstreetmap.org/wiki/Tag:shop%3Dnuts
I’d like to create that wiki page. Are there any sensible values other than “yes”, “dairy”, “meat”, “parve”, and “no”?
Could it happen that a restaurant would be kosher/dairy according to one authority and kosher/meat according to another authority? If so how would that be tagged?