A developer can simplify their React API logic by using Connectors for REST APIs and GraphQL. By defining a GraphQL schema, they can unify data from multiple sources in a single query without custom resolvers or backend logic. The process involves creating an Apollo Studio account, installing Rover CLI, generating a command to create the graph, and configuring it with the `rover init` command. The developer then creates a file called `earthquake.graphql` to define the schema, which includes types for earthquakes, properties, and geometry. A query is defined to fetch recent earthquakes with location details using Nominatim's reverse geocoder. The GraphQL query is then integrated into the React app by replacing the old API calls with a single function call that uses the Apollo Router to fetch data from the graph. This simplifies frontend data fetching without giving up existing REST services and patterns, making it easier to maintain and scale the codebase.