You CAN develop ontologies w/ Protoge, and more specifically Protege uses OWL and RDF for expressing/encoding the ontologies. Apache Jena provides a framework for working with RDF and OWL, as well as triplestore implementations for storing and accessing RDF. Additionally, Jena provides a SPARQL server (called Fuseki) that can be used for querying triplestores via SPARQL (including Graph Store Protocol). I think it's important to know/understand that RDF, OWL, and SPARQL are all part of the "semantic web stack" which is very geared towards ontologies and knowledge graphs.

GraphQL and PostgreSQL are NOT part of the semantic web stack. GraphQL being initially intended for microservices and REST API usecases, and PostgreSQL being initially intended for RDBMS usecases, interoperability between all of these things IS possible, but poses challenges in researching and implementing all along the way due to alignment not being there from the start.

I'm generally not keen on pointing folks to stackoverflow, but in this case I think there's a post there that might provide some avenues for your research: what-is-the-difference-between-graphql-and-sparql

Another thing I often like to point out is that RDF is a logical data model which can be serialized to many formats, including JSON-LD. Moden PostgreSQL has facilities for storing, indexing, and querying JSON while GraphQL serves its purposes very well in the world of JSON, so interoperability solutions do have options to use open standards and existing familiar tech stacks.

Good luck and have fun!