Normalizing said to heat the steel, above critical line, A3 and Acm lines and cooling in room temperature (cooling rate normally 500 to 1000°C/hr. For Steel, SA516, Gr70, Carbon is about 0.2% and heated about to 900°C
PWHT is heating below critical temperature(say around 650°C) and heating and holding and cooling rate are controlled(often below 100°C/hr).
For pressure vessel purpose, ASME Sec VIII, Div1, Table UCS-56.1 is normally followed. For thickness, 45mm, Div2 is suggested. Heating and cooling rates are normally followed per ANSI B31.1, Table.132.
Most of the pressure welds, requiring PWHT, are Procedure Qualified, including PWHT.
So, Normalizing and PWHT are not comparable. We need more data like hardness, grain size etc after heat treatment.