Infrastructure sets the upper limit on warship size

What is the largest warship that could realistically be built?

A very large hull is theoretically possible, but mission, yard size, docks, and support infrastructure impose the practical limit.

The theoretical scale offered is 500,000 tons, but the ship's role and the infrastructure available to build and maintain it determine whether the number means anything. Yard dimensions, docks, and supporting facilities become the real constraints. Displacement cannot be chosen independently of those requirements.