The thermostatic expansion valve controls the evaporator pressure. But system conditions will vary with time, with acceptable ranges, depending on outside and inside air temperatures.

So is it the expansion valve that sets the pressure of suction and discharge?

Sort of, but there are many tins which affect the pressures which float all over the place

I recall watching an AC tech check my ac systems and the pressure went up, the fan cut in to actually help condense some of the liquid and the pressure went down the fan cut out, the pressure went up again...

That's why the compressor on AC and refrigeration systems are usually PD pumps.

Car systems vary a lot because the inlet speed of the compressor varies so much from idle to cruising, wind velocity changes, so you size the compressor for you worst case condition and steady state operation

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"So is it the expansion valve that sets the pressure of suction and discharge?"

They are mostly determined by the temperatures of the condenser and the evaporator. If the system is operating correctly, you will have saturated mixture in both heat exchangers and the pressure is a direct function of temperature (as you stated in your first post).

je suis charlie