In Particular, the idea of the P-functional, in a simpler mechanics context already appeared in the classic book "Variational Methods in Mechanics", and was used in General Relativity (Palatini Action), as well as dilaton
theory in string theory.
The idea is two vary two functions essentially.

LOG Sobolev estimates were already crucial in the work of John Nash in the 1950's.

Some errors:
You forgot to mention that the Ricci flow approach was the culmination of twenty years of papers by Richard
Hamilton.
The new ideas of G.P. were:
1) The P- functional
2) LOG Sobolev estimates

Both predated G.P. but had not been applied to this problem.

Also, at the time of G.P.'s preprints, he was not a recluse, but a full prof at the Steklov Institute .