Unfortunately, at the moment assessments can only be sent manually. It's on our roadmap to add Automated Actions but can't say when this will be implemented. If automation is important to your integration (for example to support the top of the funnel assessments) you can take a look at our webhooks: https://docs.recruitee.com/docs/webhooks that can be configured by the customer in their company.
Partners API gives no-token access only to relevant endpoints in companies that have enabled the integration. In order to gain broader access to the API (for example to retrieve a candidate or offer details), the customer must explicitly generate and provide you with an API Token from Recruitee. At the moment only users on Scale+ plans have access to the API.