Start by asking. It is remarkable how rarely providers simply email their top consumers and ask what is hard. The people integrating with you have a precise, unglamorous list of the things that annoy them, and most of them have never been asked.
Then make the channels visible and low-friction: a public issue tracker, a forum where answers are searchable, a documented email address that a human reads, and a way to request features that does not disappear into a void. Publish those channels in your APIs.json so they are machine-readable and catalogable, not just links on a page somebody has to find.
The part that determines whether any of it works is whether feedback visibly changes anything. Close the loop out loud: “you asked for this, here it is, here is the change log entry.” A loop where everything goes in and nothing comes out stops receiving input within a couple of cycles, and then you have the appearance of listening with none of the information.
One diagnostic worth sitting with: look at whose feedback actually moves your road map. That tells you who your organization really considers the customer — and it is frequently not the developers using the API.
