The Zonai tech is definitely the influence for the Sheikah Tech we see in Breath of the Wild, but there is no connection beyond that. The Sheikah eye symbol relates to Hylia, so maybe we can use that to infer Hylia was a Zonai. That's the bare bones stuff we have to work with, and whether Hylia was a Zonai is highly speculative and likely will never be confirmed given the route the devs are going with lore for the series.
I'm hoping that the symbol is replicated by the Zonai, just as the Sheikah after them. I'm hoping that Hylia, and the other three goddesses, were not Zonai, and implanting the third eye is not where the symbolism began, in universe. But, it is a possibility that they may be Zonai, at this point. I don't like the possibility, but it's there.
More to the point at hand, it's still a precursor before we actually managed to meet one in the second game; where we are usually just told that there's history, despite not having evidence beyond dialogue.
Never, because that’s stupid. There’s no depth to a civilization that only has a name attached to it. They were nothing more than theorist bait. At least Majora’s Mask didn’t pretend that the tribe that created it was any more important than it actually was.
You realize we have many real world lost civilizations with little more than a name and a ruin or two. You call it stupid. I call it real world inspiration. And, if anything, the importance of the Zonai was understated in BotW, and expanded on later.