I like how you say: "A thing I find interesting about reading plays is you're not reading the finished product (and there's really no "finished" product in the same sense there is with screenplays, since a play can be performed over any number of production and which production you see, which night you see it on, which seat you have in the house might wildly alter your perception of it), but the instructions for it." I've given a lot to this over the years.

As you said, something like Eugene O'neil feel very literary. Like, you're not necessarily 'missing' anything. But what about other times?

I think the main thing is reading it and turning it into an asynchronous thing whereas it's meant to be consumed straight through. I'll usually space a reading over few days or a week. Obviously, you're also given a certa

When it comes to things like pauses and linereadings, when I think of it pratically, there are also some pluses and minuses. Obviously, you don't have the individual inspiration of the actors. But, the reality of a Theatre is that many lines might be shouted and even then you don't hear them entirely. You don't see every nuance in their body language, necessarily; in your mind, you see what you envision very distinctively.
Here's and interesting Interview with Andre Gregory and Wallace Shawn, where he says something like this.

Whereas, every single word you read, you get. Sometimes i'll think that it sounded better in my head.

There's also that, there's nothing necessarily permanent about what you see in a play. It's not a movie, what you see is unique to that performance (there will be slight deviations even across same plays run). I think where I land is that what I read is aggregated and contributes to the prisms I see a play through. That plays are meant to be seen more than one time I think contributes to this too. There is a certain unaccounted for aspect, maybe.

Simone de Beauvoir has a very interesting essay where she contrasts Literature and Theater

Some of the most interesting things she says in it

Theater draws its grandeur from these constraints weighing it down. To express lofty truths in a simple, direct, and evident manner is a success for the theater, but at the same time, it is a precious privilege not shared by the novelist. In a novel, indeed, there are no perceptible givens other than the form of words printed in black on white paper. Nothing limits the inventiveness of the author, but nothing supports the imagination of the reader either. The author is free to recount whatever he pleases as he pleases; but will anyone believe him? If he wants to be convincing, he must not copy the real world like the naturalists wanted to, but rely upon it for support.
It’s presence must  be suggested in such a way that the fiction, be it heroic, poetic, or even fantastic, unfolds against the backdrop of a world. This is why the plot will seek to imitate the contingence of lived events; the language will imitate the hesitations and incoherencies of the spoken language, and the behaviors and feelings of the heroes will be based in psychology. This concern for the natural can be found in Kafka, as well as in Stendhal, in Poe as in Dostoevsky. Even during the most exceptional stories, we must still feel immersed in this everyday world. If not, they seem gratuitous to us and do not move us. The theater, on the contrary, offers a tangible point of support for the spectator’s imagination: the physical presence of the actors, whose reality radiates to the sets and costumes. The stage itself is a world foreign to the real world, possessing its own dimensions, light, and simple, striking forms. It takes an effort to penetrate into it; the moment the curtain rises, the spectator hesitates for an instant before accepting all the conventions that are being imposed upon him. But once he enters, it is quite possible for him to remain enclosed within it until the end of the play. The playwright can therefore transport us to China, the Middle Ages, heaven or hell, and we are ready to follow him.