Data centers pay taxes don’t they? That money presumably goes into funding government services which would necessarily raise the local GDP

Only if the data center's task force of influencers, lobbyists, and arm-twisters are incompetent.

https://en.wikipedia.org/wiki/Tax_abatement

(Yes, in general, they'll pay some tax. Some. But they also add a wide variety of direct and indirect expenses, both fiscal and social.)