Linking outbound phone calls to a conversation or back-office ticket

We’ve tried using the Beta Phone calls but it didn’t solve our need. Here is our specific use-case:

• We get a support ticket from a customer. The support ticket involves calling a third-party person
• We want to be able to link a phone call to a third-party person to the conversation
• We are happy to even create a back-office ticket, and in the back-office ticket if we had the ability to make an outbound call to a phone number that does not belong to the customer that opened a conversation.
  • Have the recorded phone call live in the back-office ticket

We are currently doing this in Zendesk where we manage our outbound phone calls and then try to manually link the call to a conversation. But this is time consuming and adds many steps.

We didn’t see this in any of the integrated phone apps as well. Please let us know if we missed something or if this is something someone has been able to achieve.