If my primary link is down, is this a connectivity problem or a performance problem?

You should have in the GGUS ticket:
- Problem Kind: "Connectivity" , because you have a link down.
- Service Impacted: "None service affecting" or "Performance degradation" or "Possible performance degradation" regarding your topology and expected link status.

Should we report incident ASAP and then investigate or contrary?

As you want: You can wait - reasonably - to be able to open a very accurate ticket, or you can quickly open a raw ticket to give visibility to the event before starting investigating. For issue having a strong impact on the service it is preferred quickly opening tickets to broadcast the trouble.