Currently, I do not believe there's plan to expose this capability via API. That said, could you provide more context as I would love to understand more about your use case.
When installing our integration templates, we try to leave as little as possible for the HubSpot user to do. For example, we create custom properties for them, etc. Would be great to build these left side "cards" for them as well via api.
If you haven't already, I'd recommend jumping over to the HubSpot Ideas Forum and posting this idea there so that it's visible to the HubSpot product team and other HubSpot customers and developers. Hopefully this will gather more interest.
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