I created a new developer portal and app and configured a webhook to post data to a URL on a client website when a new contact is created (e.g. someone fills out a form on the site). I then used the client ID from my app to initiate the OAuth flow, which allowed me to log into the client HubSpot account and grant access to my application. Everything seemed to work correctly, but the integration doesn't appear on the installed integrations page for their account, and form submissions on the website don't trigger the webhook.
I've used the "Test subscription" option in the developer portal to test the endpoint on their site, and the test event works correctly and the JSON payload is received.