Hello Emil Blohmé,
Directly routing a custom connector through a Hybrid Connection is not a built-in feature of Azure Logic Apps. While the HTTP action provides explicit integration with Hybrid Connections, allowing direct communication with on-premises resources, custom connectors operate at a higher abstraction level, relying on the Logic Apps runtime's network context. Consequently, there's no inherent setting within a custom connector to specify a Hybrid Connection.
To bridge this gap, the most reliable approach is to implement a proxy or gateway service. This intermediary service, such as a Logic App proxy, Azure Function, API Management instance, or an on-premises web service, utilizes the HTTP action with the configured Hybrid Connection to forward requests from the custom connector to the intended on-premises endpoint.