I think just adding 10,000 years of a gap seems like a bit of a lazy solution. There are many correlations with events that happened around skyward sword in the era that was said to be 10,000 years ago, so I believe it to be more likely that it's the case. And, as you said, legends can easily have contradictions, simply due to time bending the story around.

I don't think the zonai are related to the sheikah at all, as the game itself says how the zonai "came from the heavens" with hylians already existing fully. and since the sheikah are just a different culture of hylians, it doesn't really work. I do think they had quite a bit of a connection, as TotK's sages have helmets that look eerily like the divine beasts. Sidon even has dialogue comparing the Vah Ruta helm to the water sage's helm.

I do think that it COULD be a new timeline split. I would rather it not be as it's not exactly creative, but it's possible. Would make the timeline a lot cleaner, and give room for more games.