If I sizing a spring close to the tank bottom nozzle. Should the tank settlement be included in HGR load case?

If you don't, you'd be sizing a spring without settlement, and when the tank settles, you'll have a sustained load equal to the settlement times spring rate.

The pipe or tank nozzle could fail after settlement. Or it might not fail.

If you do, you'd be sizing a spring that could be insufficient to support the pipe and tank nozzle when it's new. Or it might not fail.

If scenario 1 fails and scenario 2 fails, you might consider adding a half-settlement scenario and size the spring for that, in which case the pipe is only half-under-supported new and half-over-supported with settlement. In which case, it could be almost-failing in both cases.

Ultimately, I would expect that if you have significant settlement, you would end up with a constant effort spring no matter what, should you choose to go spring-support route.

Depending on the situation, you might look into other solutions to enhance flexibility.

Thanks for comments.

In my opinion, settlement value is needed to be included in HRG load case. Full settlement or half-settlement depends on piping layout/flexibility, stress in pipe and tank nozzle load.