Does Time Warp's ability go onto the chain at the end of the player's turn, creating an opportunity to react with Gust on a unit like Raven Bloom Student before they get the additional turn?

Ruling: Time Warp is not a delayed trigger. When Time Warp resolves, it immediately inserts an extra turn into the turn order for the controlling player. There is no opportunity to react to the extra turn effect after Time Warp has resolved.

Nuances:

• Time Warp does not use trigger templating (like "at the end of turn") and is not a Triggered Ability as defined by the Comprehensive Rules
• "After this one" is not trigger wording and does not create a delayed trigger condition
• You can react to Time Warp itself when it's cast, but not to a separate trigger at end of turn
• "Until end of turn" effects expire at the very end of the turn, so even if there were a reaction window, units with increased might from spells would still have that increased might
• The card likely works by inserting a turn into the turn order the moment it resolves, rather than creating a delayed trigger