Admins must be pre-approved in the Connected App. If not, you may encounter the following error messages when trying to launch a Conga Composer OAuth button:
"There was an error processing your request.", "You are not authenticated to perform this action."
Pre-approved users will not see Allow or Deny prompts when accessing Composer via OAuth, and Composer automatically creates a refresh token.
Users who are not part of the defined Profiles of Permission Sets will be denied access.