"Amid growing evidence that the massive upsurge in tourist apartments is driving rents up and residents out, the city has launched a crackdown on illegal, unlicensed apartments, and Airbnb, the dominant platform, is in the eye of the storm, although not the only offender."

Sure looks to me like the author is suggesting that Airbnb is is in the center of a storm causing damage to the city of Barcelona.

If you are in the eye, then you've had the strongest winds already hit you and they will hit you again as the eye passes by, not that this defends the metaphor.

"Eye of the storm" refers to the center of a hurricane, which, yes, I'd relatively calm. As a metaphor it is often used to evoke the calm surrounded by chaos aspect, but sometimes (though less frequently) used to evoke the center of the chaos without particularly evolving the calm ("ground zero" is an alternative metaphor for the latter use which lacks ambiguity, but seems to be less used, IME, since 9/11.)

things are probably pretty calm at airbnb headquarters.