So, calcing the energy released by R'lyeh sinking. For a long while I refused to do so, due to lack of concrete timeframe, but I think I got enough proof to assume a quick timeframe.
Well first of all, said timeframe. It looks obvious enough that none of the Cthulhi or Cthulhu himself could react to it, since tons of them were trapped under the ruins. Furthermore it's often treated as sudden and not gradual. Since I can't use their reactions time or FTE to calc it, I'll just use 1 second.
For the distance traveled, the city sank from the surface to the bottom of the seas. The average depth of the seas around R'lyeh supposed position are apparently 4828,03 meters deep, so we now have the speed, 4828,03 m/s
The size and mass of R'lyeh naow. Well first of all, it seems like an accepted calc, well, accepted that Cthulhu's spawn could be compared in size to the giant mountains. Now Cthulhu not only shouldn't be much below his spawn in size, but he has been described as being like a mountain several time. Note that said giant mountains easily dwarf the himalayas in size, and that even a small part of the City was large enough to hold Cthulhu in it. So R'lyeh should be much MUCH bigger than mount Everest, and possibly the Himalayas.
However I haven't found the weight of the Himalayas, so instead I'll use Everest's. Which was estimated to be 6399000000000000 kg.
So, slapping all dat shit into KE we have blargh 7.457994084203954e+22, Country level. Apart from Cthulhu himself, most Cthulhi survived the sinking. Even if you don't believe they tanked the energy, they did helped building R'lyeh, who survived the impact. This means all the races who scaled from Building to MCB scales to Country now.
Alternate calc. The Mountains of Madness were 10668 meters high, while Mt. Everest is 8 848 meters high. So they are 1.2056962025316456 times higher. So, 1.752724587963629784504775484292320984587426146816 times heavier. Which means R'lyeh is at the very least 11215684638379266.991046058323986561980374939913475584 kg. So 1.3071809608271561e+23 joules. No upgrade there.
EDIT2: Using Ythogtha's calc'd total mass, which is 126859472732160000000 kg, gives out 1.4785391423061137e+27 joules. So Continent level+.