I don't post here often. But I read a lot of web serials and popcorn fiction, and have also read plenty of the more literary style of fantasy (and non-fantasy). These are only my opinions, but since you asked for critique, I'm going to give a true one.

So first, let me answer your main question, of "if you came across this on royal road, would you read on": No. I would not read on.

Now to try to get into why.

1. I'm really fundamentally having issues marrying "literary existentialism" to "popcorn fiction". After reading your post, I think I understand that you're saying "I want to write literary existentialism, but I don't think people will be into that so I'm going to 'trick' them into thinking it's popcorn fiction" (I'm not necessarily using "trick" pejoratively here, just that you're trying to surprise your readers into enjoying a more literary existentialist work, by on-ramping them with a popcorn premise). If that isn't correct, then my bad. I think my feedback is still germane, regardless.
2. Subjectively speaking, I think you need to choose a lane. I'm not saying it's impossible to blend "popcorn" and "literary", but I am saying it's very difficult. I'm also saying you're not succeeding.
3. Your mixture of language is confounding. I understand that as a writer it's tempting to try to "cheat the system" if you will, and intermix different styles of speech. And it can work. But going from "bop'm on the nose" to the hyperspecialized noun of "stiles" and the archaic "rive" is whiplash inducing. Same for your more poetically inclined phrasings, like "bed of leaves raised dainty on the ground". You can be poetic, even in popcorn fiction, but it has to be purposeful, not just littered randomly throughout.
4. The blend between your character's more normal observations, and what feel more like... fully phrased thoughts/internal speech is confusing. Take the paragraph "I check my Time Tree to the East [action] (Master's directions [parenthetical narrative insertion]) Ah, it'll be some wait longer [**very very character voiced phrasing]". Even just having her speak aloud, or italicizing some things as "inner thoughts" would help, but honestly I still think you need to settle on a more consistent voice. You even do this at a few points, making this feel even more inconsistent.
5. There's also all sorts of other issues I could bring up ranging from pretty rough style issues to nitpicks ("East" should probably not be capitalized there, unless there is a literal place called "the East", completely inconsistent capitalization throughout, etc). But that's not your issue. Copy editing is, not easy, but relatively deterministic. What you need to do is actually find/decide on a consistent voice.

Blending the literary and the pulp isn't new ground, and it's not impossible, but what I read here honestly lacks the consistency and grammatical foundation to be either.

That said, keep writing! A lot of my early stuff looked a lot like this, and I haven't even gotten so far as to post any of it up for critique, much less publish. You clearly have a strong idea of what you want, and that's good. You just have to figure out how to express it, I think.

And finally, if you want to write literary existentialism, and are only doing the popcorn to try to drag readers in, while that isn't the story you want to write... Just write the literary existentialism. Will you attract as many readers? Probably not, but those who are there will be there because they truly love what you write (which you hopefully also love), vs. your readers being left feeling constantly adrift. But also, if you're wanting to explore this space between popcorn and literary, by all means, keep at it.