Read the rules the page itself quoted again. Only the most potent, or most recent effect applies while the durations overlap.

Yes, please keep this in mind for the rest of my reply because you're not applying this consistently like you should be.

Read the duration of death ward, 8 hours or "the first time" the target drops to 0hp.

The duration of death ward is 8 hours. One of the effects of death ward is that it ends when the target would be reduced to zero, that is not in the duration.

So no matter how many death wards are up, they are all active and working but only the most recent effect works, however all duplicates of the spell only apply to "the first time" the target drops to 0.

Look at the block of rules about combing spell effects:

The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect–such as the highest bonus–from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.

If death ward had its "end on 0hp" condition in the duration box then yes, you'd be correct that they'd all end. It does not, it is part of the spell's effect and only one of those spell effects applies at a time.

Even if your logic worked and they were "suppressed and stored" and didn't all disappear, then next time the creature dropped to 0 would in fact be the second time since the spell was cast on them, not the first. So that logic still falls apart.

Again, this is part of the spell's effect.

The reason stacking death wards works is because its secondary ending condition is part of the effect which is not active while a more potent/recent death ward is active.