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Doesn't magnetic pole shift due to fluid dynamics in Earth core? Wouldn't that also affect gravity field?

Yes it does but we also have satellites mapping those shifts so it could be accounted for. The big question is are those fine grained enough to resolve the errors in modern INSs.

Wouldn't that then require communication with those satellites to receive the shift/drift info? Doesn't that eradicate the point of a navigational system without reliance on GPS/satellites?

Or is the drift is so minor that this quantum navigation system can operate for up to 6 months without sufficient core drift alignment calculation?

No idea but there are low bitrate coms available to submarines that could update that data maybe. The changes should be pretty slow at the bulk scale.

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