504 Time-out error on Select application form submission

Problem/Motivation

I'm trying to connect the site to Acquia. On 'Acquia Subscription setup' (/admin/config/system/acquia-agent/setup) page I click 'Authenticate with Acquia Cloud' button, pass authorization and redirect on 'Select application' page (/admin/config/system/acquia-agent/configure). Then I choose a subscription from select list and press 'Set application' button. The site starts loading and crashing with 500 or 504 error after some time.

Reason: there is a function _acquia_agent_cloud_api_request() which runs on form submission. It makes an API request to Acquia:
/applications/{applicationUuid}/settings/keys
(https://cloudapi-docs.acquia.com/#/Applications/getApplicationLegacyProd...)
In my case this request always returns 403 error with the message: "You do not have permission to access these product keys."
This case is not handled by the logic and the function loops, resulting in a timeout.