Does Mystic Vortex make the Diana Legend pay 1 power?

No. Mystic Vortex only increases the cost of playing cards that have [Reaction] during showdowns there — it doesn't touch the Diana Legend (Scorn of the Moon) or its activated ability.

The Diana Legend isn't a card being played: Legends are established at the start of the game and are never played during regular play (Rule 174.2.a). Its [Reaction][>] is just the timing permission on its activated ability, whose only cost is exhausting the Legend ([T]) — it has no Power cost for Mystic Vortex to increase. Mystic Vortex's [A] surcharge applies to Reaction cards (including Hidden ones) played from hand or the Champion Zone, not to Legend activations.