Regarding @Leo Liu's answer, I have tried it via api version 7.1 and I can set fields: AutomatedTestName, AutomatedTestStorage, AutomatedTestType but I can't set AutomationStatus field to 'Automated' value, because there is not the value in the drop down list in ADO.

Response:

"errorMessage": "The field 'Automation status' contains the value 'Automated' that is not in the list of supported values"

It seems that the binding can only be done via VS - then AutomationStatus field is set automatically to 'Automated' value.

This is a very big disadvantage because if we have a lot of tests to associate, we have to do it manually.