Zero Sequence current Understanding
Zero sequence is not DC.  The zero sequence component in each phase has the same magnitude and phase angle. They are a set of phasors that rotate counter-clockwise just like all positive frequency phasors. Below is slide with overview of the symmetrical components. Note that i didn't attempt to use the exact real component phasors for the phase quantities shown - i'm just trying to show that any balance set of 3 phasors can be decomposed (transformed) into 3 balanced sets of phasors.

There is no connection to the zero-sequence neutral bus for the wye-grounded/wye-grounded (Ynyn) transformer because the neutral currents are equal in per-unit.  The zero sequence ampere-turns in primary balance those in secondary.

If you added a delta tertiary then the zero sequence ampere-turns between primary and secondary would not balance - and now you would have a connection to the zero sequence neutral bus as shown below.  Note that in these figures the ground symbol in the zero sequence means connection to zero sequence neutral bus.

EDIT: Adding a few slides showing complete symmet model of Ynynd bank for clarity. Here i take the test data for the three-winding bank and convert it to a T model (i put it on 100MVA but you can use whatever is convenient). This example doesn't have the neutral impedances but you can see where they go per above figures.
Transformer test data is usually provided as pair-wise impedances.  These are then converted to T model as below.  Note that the zero sequence test data is often different (may have to request it from the manufacturer as usually nobody cares about it but relay engineers).

Below shows how the T models are inserted into the symmetrical component networks (i show source Thevenin's on each side which you can ignore).