My opponent is attempting to move to the end of turn from an open game state. Do I get an opportunity to react?

No, you do not get an opportunity to react simply because your opponent is ending their turn.

According to the rules and established FAQs:

• Reactions require a chain: You can only play a reaction when a chain is already open (a "Closed State"). If your opponent is simply ending their turn and no triggered abilities or other effects are placed on the chain, the state remains "Open," and you have no window to play a reaction.
• No "End of Turn" reaction window: There is no "end of turn" opportunity to play reactions that prevents your opponent from taking further actions or transitioning phases.
• Opponent control: The active player controls when chains open during their turn. If they choose to end their turn without starting a chain, you do not gain priority to act.

As stated in the RiftJudge FAQ (ID 6113): "You cannot play a reaction when changing phases. You can only play a reaction during an opponent's turn if the chain is not empty and you get priority, or if there is a showdown and you get focus."