Chat conversation transcripts can be logged to Salesforce records via the Create Task node in Chat journeys, but there is no equivalent for HubSpot. When a chat session ends, there is no way to write the transcript or a conversation summary back to the associated HubSpot contact record.
Admins using HubSpot as their CRM should be able to log chat transcripts or summaries to the corresponding contact record after a conversation, consistent with how this works in Salesforce today.
This has already blocked at least one evaluation, where the lack of HubSpot transcript logging was a confirmed gap during the sales process.