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Since Turkey is paying you, taxes are due to Turkey on the income, not the US government. CA was not a part of the treaty so they want your share as you are a resident there to help with that government

There are too many laws with minor variations for the program to ask everything  This is considered a self prepared return and the responsibility lays with the taxpayer..

Amending returns for accuracy is always recommended.

To add the CA income, since your income is similar to pension, I would add it on the screen for pension adjustments. CA doesn't have a place for easy entry of foreign income not taxed by the federal. I think they should be happy you are adding it and will understand that this is the best solution available.