1. Raju Soni has admirably pointed out the case. True, the difference in the formulas (operating vs. seating) must be only the value of "Total moment acting upon the flange, for the operating condition or gasket seating condition". And yes, for gasket seating, the total flange moment is based on the flange design bolt load, which is opposed only by gasket load.

2. It would be the moment for seating condition greater than the moment for operating condition, leading to a J index over 1? I made some numerical tests for 150# flange cases. The moment acting upon the flange for seating condition was less than the moment for operating condition….so for certain B16.5 flanges I would say they are not over-stressed in the seating case and ok for both seating and operating, despite the Caesar calculator predictions! Moreover, looking to the mathematical relations there is a big chance that this remark would be true for a wide class of flanges 150# to 400# with spiral wound gasket, so I cannot confirm there is an incompatibility between B16.5 and ASME VIII.

3. In fact how does Caesar calculate the moment for seating condition?
In my opinion, it would be simple calculated taking into consideration exactly what Raju Soni highlighted: considering the reaction on gasket for seating condition that should be exactly W0 - the flange design bolt load.