With the 7.62x53R, or 7.62x54R, the old Russian, why is it so potent. It has similar case capacity to the 308, but many data references place its capabilities right there with the 30-06. Typically, I would attribute this to a higher working pressure, but this is an OLD cartridge. Why or how is this the possible?

You will find that up to around 165 grains, the 308 is up with the old '06 and none of these catridges, 308, 30-06 or 762x54 are dogs.

As for the strength of the Mosin action, I recently did a blow up test on a 1945 dated soviet action. I won't openly tell you what loads DID NOT blow it up or even set the lugs back, but you can damned near shoot anything in it without any fear whatsoever. And unless the casehead lets go, escaping gas is a moot point. The action finally did let go with 31 grains of Bullseye under a 147 gr. Russian FMJ and even then, the receiver held like a T34, it was the bolt head that suffered the most but it all stayed in place, the shooter would have had to change his drawers but that's about it.

Capacities measured to base of neck/case mouth, in grains of water
308Win 49.9gr/55.6gr
7.62x54R 51.3gr/60.9gr
30-06 61.0/68.2gr