As stated, you do not want any sort of chemical competition for the AW package on new metal surfaces.
Modern engines that are factory filled with synthetics are all either OHC or Roller Cam'd.
You rebuild a flat tappet motor (older car, truck, boat or tractor) and you use good dino oils with decent add-paks... You don't and you will be doing it again.
The thing becomes more involved when you get to Iso-Syn and severely hydro-cracked dino oils... They are as good as many synthetics (99% are a blend anyway), but work OK for break-in
And then again, it all depends on what cam lube you used during assembly... If you used Crane Cam's goo, or Sta-Lube moly paste, you should be good to go with most name brand oils. You use the red slime from Comp Cams and let the motor sit for 24 hours and you may be praying there's enough left to do its job (it runs off)...
As usual, it's the combination of parts at hand and work-flow that will determine if you need something special... There are rebuilt engines sitting in warehouses for months that will have to fire and go. For those I'd use best quality dino oil for fist 50 hours or so. If they live that long, you can pretty much put anything you want in there and drive on