How would Kai'sa Evolutionary and the legend Jhin Virtuoso interact? If I conquer a battlefield with Kai'sa, then play a spell from my trash that costs four energy or more, can I banish the card (with Jhin) instead of recycling it (with Kai'sa)?

To determine the interaction between Kai'Sa, Evolutionary and Virtuoso, we must look at the timing of their triggered abilities and the specific instructions on their cards.

1. The Sequence of Events

When you conquer a battlefield with Kai'Sa, Evolutionary, the following sequence occurs:

1. Conquer Trigger: Kai'Sa's "When I conquer" ability triggers and is placed on the chain.
2. Resolution of Kai'Sa's Ability: As this ability resolves, you choose a spell from your trash and play it. The spell is placed on the chain.
3. Spell Resolution: The spell resolves normally and is placed in the trash.
4. Kai'Sa's "Then" Instruction: Kai'Sa's ability includes the instruction: "Then recycle it." This is a mandatory game action that moves the spell from the trash to the bottom of your deck.
5. Virtuoso's Trigger: Virtuoso's ability ("When you play a spell...") triggers after the spell has finished resolving.

2. Can you Banish the spell with Virtuoso?

No, you cannot banish the spell with Virtuoso in this scenario.

• Timing Conflict: Virtuoso's trigger condition ("When you play a spell") is met only after the spell has fully resolved. By the time this trigger is placed on the chain, Kai'Sa's ability has already finished resolving, which includes the mandatory instruction to "recycle it."
• Zone Change: Because the spell has been recycled (moved to the bottom of your deck) as part of Kai'Sa's ability resolution, it is no longer in the trash when Virtuoso's ability attempts to target it. Virtuoso requires the spell to be a valid target to be banished; since the card has moved to a different zone (the deck), it is no longer a legal target for Virtuoso's effect.

Summary

Kai'Sa's ability is a single, cohesive instruction set: play the spell, resolve it, and then recycle it. Because the recycle instruction is part of the resolution of Kai'Sa's ability, it happens before Virtuoso's "When you play a spell" trigger can even be placed on the chain. Consequently, the spell is moved to your deck before you have the opportunity to use Virtuoso to banish it.

Note: I could not fully verify this ruling against the retrieved rules.