Mike, thank you for the direction.
Craig, thanks a lot for the detailed, clear and friendly explanation!
The setting "Devices per Initiator Port" in our StoreOnce is 4 per FC port (as shown in the below picture). That would double to 8 as you explained because we have two FC ports zoned into our Veeam server, and we should see 8 "HP StoreOnce CoFC SCSI Processor Device" entries in Device Manager. (Please correct me if I am wrong.)
In light of the above, our Veeam Catalyst Backup Repository setting "Limit maximum concurrent tasks to" should be set to 8 instead of 4 (our current setting). If that number is set too low, Veeam would warn us "number of devices per initiator port in Catalyst over FC settings is too low" when we proceed to add the backup repository. (Correct me if I am wrong.)
Strangely, unless my memory fails me, I remember we did increase this number in Veeam and the message still prompted though.
I will revisit the infrastructure later next week, so I will try again and report by then.