Hey @RDufour4 hope you are doing well.
So for know the only messages you can display in the customer portal
are the emails sent.
I think HubSpot support team uses a different support system so this is why we cannot recreate their interaction.
You can find more info of how to use the cusomer portal here.
If you have CMS Enterprise you have Membership pages
and the you can put more info, for example, have a HubDB table with all the tickets, all the conversations, or even information from outside HubSpot that you want to display.
Of course this is a 100% custom thing to built but is a great way to use it the way your company needs.
Hope this helps.