We have a particular edge case in our system configuration where we have inbound "out of business hours" calls and these are handled differently, as this is forwarded to a physical mobile. When we try to query the metrics via the endpoint GET /api/v2/analytics/conversations/CONVERSATION_ID/details and we only get information regarding the performance of the flow. If we were to look into the call manually, it has a Dialing time which is not shown on the JSON output from the API call. Is it possible to check wether this is not a feature or i'm using the wrong endpoint?
Not knowing what metrics you were trying to extract, it's hard to comment.
But in the flow you describe, I understand your call is transferred to an external number - which is not assigned to a resource defined in Genesys Cloud (a user/phone) -> external participant in the conversation (participant with purpose=external).
In this case, most of the metrics available in conversation details will not apply. Metrics related to handle time, talk time, ... are only effective for a user/agent.
In your case, you'll probably only have a nConnected and tConnected on your external participant (if the call is successful - tConnected should be accurate if your are performing a bridge transfer).