What does Leovold, Emissary of Trest & Teferi's Puzzle Box do to opponent's hands?
Even though the phrase &quot;beginning of the draw step&quot; suggests otherwise, those abilities trigger after the turn-based action of drawing a card for the turn.

504. Draw Step
504.1. First, the active player draws a card. This turn-based action doesn’t use the stack.
504.2. Second, the active player gets priority. (See rule 116, “Timing and Priority.”)

Regardless how many cards Player 2 has in this case, they will draw a card, then Teferi&#39;s Puzzle Box triggers, eventually resolves, then has that player put all cards on the bottom of their library.
Leovold, Emissary of Trest will prevent them from drawing any other cards, as they've already drawn a card this turn.