ARP/MAC Tables Not Updating on Core Switches After F5 LTM Failover (GARP Issue?)

...that means that shared MAC would only be learned on one Port-Channel interface.

Right. Or to put it a 100% correct, it should only be learned on one vpc at the same time.

When failover occurs, you're saying the new Active will start sending packets including the shared MAC and the switch CAM tables should update to reflect the MAC now being on a new Port-Channel interfaces (thus no need for GARPs)?

Right. I think it actually will send GARPs nevertheless, but those are not needed to update the ARP tables on all neighboring devices, those can be left unchanged. Thus, the network will be less error-prune to the N7K not learning the ARP update (regardless of the reason why that happens...).