Hi,
I think that the summary of the question is: Synthesis is done using which PVT lib ?
My answer to this question is, the lib should worst case: P=SS (slow slow), V=minimum voltage, T=Maximum temperature (this can change in recent technology nodes)
To answer why using this lib ? Because, in synthesis we need to have a clear setup timing (worst case affect setup time and best case affect hold time)
So after performin synthesis we need to have no timing violations in setup time, because they cannot be fixed in place & route. Hold time cane be fixed by P&R tool by adding buffers.
In P&R all libs are used.
Does this answer the question ?
Regards