Does Narset, Parter of Veils stop opponents from drawing replacement draws from Sylvan Library?

Narset, Parter of Veils has a static ability that reads: "Each opponent can't draw more than one card each turn." This creates a continuous effect under CR 613 that simply caps the number of cards an opponent may draw in a turn to one (CR 630.8 covers draw-restriction effects).

Sylvan Library's triggered ability lets a player draw two additional cards at the beginning of their draw step, then requires them to either pay 4 life per extra card kept or put the extras back on top of the library. Crucially, those additional cards are drawn — they are not replacement effects that replace a draw, they are genuine additional draw actions (CR 120.1). Each draw is a discrete event.

Because Narset prevents an opponent from drawing more than one card per turn total, the opponent simply cannot legally draw the two extra cards Sylvan Library would provide. When Sylvan Library's trigger resolves for an opponent, that opponent has already used (or will use) their one permitted draw for the turn during the draw step. Any attempt to draw additional cards beyond the first is prevented by Narset's restriction. The player still puts no extra cards in hand from those draws.

Practically speaking, Sylvan Library becomes nearly useless for opponents while Narset is on the battlefield: they draw their one card normally (or via Library), cannot draw the extra two Library offers, so there is nothing additional to pay life for or return.

Example: It's your opponent's turn and Narset is on the battlefield. Sylvan Library's trigger resolves. Your opponent has already drawn one card in their draw step. When Library tries to have them draw two more, Narset's effect stops both draws — the opponent draws zero additional cards, keeps nothing extra, and pays no life.