Vader, otherwise, tarkin.

Supreme Commander Gilad Pellaeon.

In terms of infrastructure, probably Tarkin. Militarily, there is no replacement for someone like Thrawn.

However, in both continuities (that is, Canon and Legends) Sidious has the secret plan to replace his mostly mundane and technologically oriented Empire with a more Force-focused one (in Canon, the Final Order and in Legends, the Dark Empire). I think that this clearly paints the picture of Vader being far more important to Palpatine’s long term plans for the Empire than either Thrawn or Tarkin could ever hope to be.

Vader is because he was going to be Palpatine’s most valuable ally

In terms of actual operation, definitely Tarkin. Vader didn’t do much in terms of keeping the Empire actually afloat.

Vader. No Vader, no Star Wars.

The fear Vader inflicted on the galaxy alone probably prevented the rebellion from being much bigger than it was

Ofc Vader