Spatial Interdependence and Posterior Predictions in a Gaussian Process model

A quick followup with what is hopefully a quick question for @paul.buerkner, to make sure this is clear.

I can see from this and the brms documentation that posterior predictions (posterior_epred and related) include autocorrelation. Is that also true of GP terms?

Apologies if I’ve missed something here. It seems like the spatial correlations are not showing up in the predictions, but I might also be missing something conceptually.