When water from the (upstairs) bathroom shower or sink is released into
the grid outside the kitchen, a noxious, sulphur/garbagey smell
overwhelms the kitchen and part of the living room.

You might have an unused trap that has evaporated out due to non-use. This
could be for a washing machine (that was later moved into a separate
utility, for example) or a water softener that the previous residents took
with them.

If so, the fix is to either refill the trap manually every month or two, or
to remove the trap altogether.

Christian.