GeoServer Cloud is a cloud-native version of GeoServer built using dockerized microservices. Release 2.27.0.0 from two days ago adds support for input data in GeoParquet DataStores. This broadens the existing support of cloud-native input data formats which already encompassed FlatGeoBuf and Cloud Optimized GeoTIFF (COG).
Not a GeoServer (sans “Cloud”) expert, but from what I could gather from the docs and the extensions page, GeoServer proper does not seem to support GeoParquet, FGB, and COG (but, for example, a directory of shapefiles).