The critical point by definition is on the equilibrium curve, and thus requires a closed system. Gas turbines (e.g., jet engines) are open systems, however.
Pressure ratio misconception.
The quoted figure of 60 is the maximum attainable in cruise. It's called OPR, O for overall, which takes into account the increased compression from the ram air (the air being rammed into the inlet at say Mach 0.85). So at takeoff where the atmospheric pressure is higher but the forward speed is slow, the OPR is a figure lower than 60. (But since it's an open system it wouldn't matter if it were higher.) A prominent example of the additional intake compression was the Concorde:
The overall pressure ratio for the powerplant at Mach 2.0 cruise at 51,000 ft was about 82:1, with 7.3:1 from the intake and 11.3:1 from the engine compressors.
Is air (fluid) in the high pressure regions of a jet engine supercritical?
If you mean exhibiting both the gas and liquid phases, then again no.
This only applies near the very cold critical point, and going around it (seamless phase change) will require massive cooling. For a jet engine, even considering supercritical conditions, gas will still behave like a gas.