How much choice is preserved in Gitik models of ZF?

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In a Gitik model of $\sf ZF$ choice is obviousely lost since all uncountable cardinals are singular and of cofinality $\omega$. Now that choice is lost doesn't by itself entail that weaker forms of choice are not preserved.

Up to which stage in the choice spectrums $\sf DC_{< \kappa}, \sf AC_X^Y(Z)$ choice can be preserved in a Gitik Model of $\sf ZF$?