Russians are world champions in STATO engined missiles since 1963 (when Krug and Kub SAMs have been created), so they don't need help from losers
Vympel has been studying STATO R-77 (as R-77PD) in the 90-s when Russian chemical science and and industry was almost in ruines after Yeltsin's "reforms" and could not create programmable melange fuel charges.
As well as Americans, who have studied AIM-120D first as STATO missile but then (at the same time with Russians) have managed to create PMC SRMs which allowed them both leave STATO for AGMs and ARMs (like Russian Kh-31 family).
STATO problems with intake blowbacks do not depend on fuel type, but on the factof air intake presense itself
I've proposed you to draw supersonic chockwave cone lines on this intake not to just make you to do useless thing but to make you see the angle by what those chockwaves lay into the intake and think about how those high AOA maneuvers will change chockwave angles in the intake and what can it cause in each case.
So, STATO engined missiles are not for air combat but just to hit non-maneurable targets. But why to use them even this way if there are rather more effective ones (like R-33/37 and Item 810 family)?