Would you mind clarifying what "activate the HubSpot tracking API" means?
If your goal is to monitor Squarespace pages within HubSpot, you will want to install the HubSpot tracking code into your Squarespace pages by following this guidance.
Regarding the form, these articles will be a good starting point :
Thanks! I mean the tracking cookies. I have read through the articles you shared but can't figure out if the SquareSpace forms meet the requirements for hubspot "Non Hubspot forms".