Our Product org uses Productboard but expects end users to go a step further after creating a Note and link insights from within the Note mapping to Product feature sets, as well as establishing the “Importance” while doing so.

The Gainsight integration does not appear to allow users the ability to go this extra step, therefore use of the connector would require users to create the Note through Gainsight and then still navigate to the Productboard to create the insight links, which doesn’t save any effort on the part of a CSM.
I fully understand this would likely be a herculean effort to accommodate - unless something already exists of which I am not aware (though I haven’t seen it documented) - but without this capability (and the limitation of only being able to sync records that were logged through Gainsight) the usefulness of this integration for us is going to also be limited.