Does the Delaware Statutory Trust have any effect on the step up basis in California?

As a pass through entity, no difference should occur.
The step-up basis is when somebody dies who owned a property. If the person bought the property in 1955, their relatives would pay Capital Gains Tax on the difference in value between 1955 and 2023 if the relatives sold the property. Step-up basis would prevent this and allow you to sell the asset at the current value at the time of the person’s death.
The only Trust that would not qualify for getting a stepped-up basis would be an Irrevocable Trust. That has a basis on the death of the Grantor.