I still haven't read existentialism, except for Louis Lavelle, which is not very famous, but has a great philosophy. So, I think I'd say yes to the question.

E.g.1: there has to have formal, fixed rules of Nature, or else no science would ever evolve from one generation to another. We found Newton didn't have the complete equations, although they still work within a certain scope. But the fact we could change it to Einstein and Planck's model means the real laws themselves are fixed. (although they're most likely not Newton's, nor Einstein or Planck's, and maybe we never even get the complete version of it, but the fact our laws predict true events means they both shows the true laws exist and points to them).

E.g.2: The same way, each male has a lot of common features. If it wasn't so, you couldn't use the knowledge of one man to another, so each man you meet would be the first and only one, and that would be like every person speaking a language on their own, completely unrelated one another, thus incommunicable. That's literally impossible. Even more: what we know about a man we can apply, to a certain degree, to a woman. Because in a more general way, both are human beings. You can expand this and basically say that the same possibility of analogy and metaphor human mind can do proves the fact that everything is connected in this "more abstract category" which we call the Being. (Being is basically a word to call the most abstract aspect of an object, which everything necessarily has in itself. So there's me, I'm a man, that is a human being, that is an animal, that is living thing, that is an existence, that is a being: each category gets more abstract; we may think about it in another terms or more terms, but Being is the most abstract nonetheless).

So there's essence, which is this structural aspect, and each thing grabs a lot from each of these categories, from the being to itself. The point of the self, though, is the existence. We may say it doesn't change the essence, because a human man can't do what is inherently impossible to it. But we can do things that are unlikely. For instance, a man can decide he is a woman, and then change many of its atributes. He may look a lot like a woman, but it unfortunately doesn't change the fact that in reality he is a man who opened such possibilities, which weren't very common before 20th century. Because of that we may try to say "existence changes essence", but it isn't true. We may even accept as a woman, in existence/phenomenical world, but it can only be so because man and woman are both from a very close structure. If a man, though, for a different reason would try to truly identify with something else, whatever it is, that would be much harder, though.

Is that nondualism more similar to a mind-only kind or more like a matter-only variety? In the former, I feel like meaning is ontologically fundamental in some sense while in the latter meaning doesn't exist, and is just a figment of illusory experience---meaning is just overlaid onto an otherwise meaningless fundamental reality.

That being said, even in a materialism-only view, one can say that meaning is still there in an information-theoretic sense. Reality has real objects and structure, and an organism is sensing that and representing it with patterns of neural activity. When said organism communicates with another organism, there is an ontologically real correspondence between their neural activity and the patterns in the communication with the actual real world they are sensing and communicating about. That is the meaning of their communication, it "means" the particular arrangement of material reality.

I am more of a mind-only type of nondualist though (at present).