A PDF's pages aren't independent files stitched together — they're entries in one shared table that a reader walks through in order. Splitting means building a brand-new, minimal document around whichever pages belong in each result, so every output file opens on its own with nothing missing and nothing extra.
That's true whether the split is one page at a time, a range you typed, an equal chunk size, or a byte budget — the mechanism is the same copy operation each time, just with different rules for where to draw the line. Because it's a structural copy rather than a re-render, every result looks and behaves exactly like the corresponding pages in the source file.
Everything runs in your browser. Your file is never uploaded, never queued on a server, and never deleted from one — because it was never there.