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Excellent suggestions. You may wish to add to a new or existing thread in HubSpot Ideas.
You'll typically get much more traction from the HubSpot Community AND the Ideas Forum is where HubSpot Product Teams monitor suggestions for popularity -- i.e., VOTES!
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You can use Dossier, one of the certified HubSpot integrations, to send all new client emails or chats to Slack channel(s). You can map specific accounts to their own Slack channel, or have all chats go into a single Slack channel.
This is useful if you want to automatically send all requests from clients in an application (i.e. a support widget embedded in an app), or send all chats to a website directly to a Slack channel.
See https://www.hubspot.com/integrations/dossier and then visit the Dossier site. If your use case is that customers use chat (on a website, or in an application) to contact you, sign up with Slack, then connect HubSpot and your email. If your customers contact you on email, then sign up with email, connect Skack and HubSpot.
All Slack chats are automatically synced to HubSpot CRM.