Re: esd for vdd and vss pins
A well done ESD pad library would include the core clamps
that complete the current loop. Could be GGNMOS, could
be active triggered, could be the two combined. A back
diode from vss to vdd should be part of the core clamp.
You may find these as part of corner bussing cells, too,
depending on who did the architecting and what kind of
library (std cell with common pads, this is likelier; analog
with bare pads only, not so much).
You could look at the ESD or I/O libraries documentation
and find out whether such a thing is provided. If not,
welcome to the fun.