This question might have a simple answer I do not know. Why where there is a high pressure drop across a PSV or PCV, they inject glycol or methanol upstream of the device?

If there is a high pressure drop across a valve in gas service, there is an accompanying temperature drop. If that temperature drop is sufficient, you can get hydrates downstream of the valve.  The glycol or methanol injection is to prevent that.

I also have not seen this for a pressure relief valve (PSV).

The hydrate formation temperature depends also on pressure, downstream of your PSV the pressure is very low (usually less than 5 bar) so the hydrate formation temperature is much lower. For you PCV the flow is continuous and the pressure will usually be higher. This may be the reason in your case.

About injection methanol upstream of PCV.  Once we had accident with PCV, because of leaking it hydrated. One of possible solution this problem proposed to inject methanol upstream of  PCV.

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