What's appropriate depends very much on why it is that you want to determine the valid possible measurement types.
For example if you're designing a user interface for software it would likely be sufficient to categorize it under "Other", e.g.:
- Liquids: fl oz, gal, cup
- Powders/Grains: oz, g, lb, cup
- Other: pieces, items, leaves
You could also, in an organization like that, just have a selection for "count" or "no special units" or something to signify that an additional explicit unit is not required, and that the unit is implied by the ingredient itself:
- Flour: 20 g
- Milk: 0.5 l
- Eggs: 1
Because in that context you're never trying to construct the actual sentence, "an eggs is a _____".
If you're loooking for a description and you don't care how verbose it is, there are plenty of descriptive phrases:
- An egg is a countable item.
- An egg is a distinct object.
But those may be too awkward and clunky for your purposes. There are also things like "an egg is discrete", which I suppose works, although it is not a noun, but of course would look very odd and out of place in the context of a recipe. You'd never see terminology like that used in, say, a cookbook. You could also say "an egg is an object" which works but, of course, is too vague.
If you say "an egg is countable", that probably will have the highest success rate of being understood while being the least awkward possible. If you must stick precisely to your example forms, "an egg is a countable item [or object, or ingredient]" works. Still slightly awkward but probably the least of all the evils.
I would sit back and think what your end goal is, then you'll be able to make the most appropriate choice. In particular if you're doing some sort of user-interface thing, a slight reorganization (e.g. categorized units above) might make this word choice unnecessary.