Yes, the newest shift in algebric geometry is using homotopical ideas baked directly into it, either through the use of motivic homotopy, which declares the affine line used in algebraic geometry to be now like the interval was in the usual classical theory of topological spaces, the other approach on the other hand does use infinity-categorical methods, the two approaches intersect in some form as they both rely on heavy general machinery.

They both have been going around for a while tho, at least 20 something years or so, but math is slow like that and there was a lot of work to do so I think its only been more or less a recent thing that it exploded a little bit ( its still overrepresented on the internet tho ).