What is meant to populate the Serviceroot "Product" property

Well, the intent was just that - the actual product that you're talking to, so in your list, I think the HPE unit is correct. But I can see that "the product represented by this Redfish service" could be interpreted as the firmware or management "product" that is providing the HTTP service! So the Dell and AMI aren't totally wrong, either.

I'll bring this up with the group to see if some clarification is needed - but I suspect that even if we make a clarification, the vendors may be hesitant to change those values as customers are likely already coding for those values, just as you're trying to do. But if we can get OpenBMC to provide a useful value, then that may be sufficient, as I would expect your code would be able to determine what to do for any "Integrated Dell Remote Access Controller" instance you find??

Note that there is also the "Vendor" property which may help your selection logic - especially if it is supported on the ODM units (and returns something other than "AMI" in all cases).

Jeff