I think the long now foundation tries to promote it to raise awareness and get people thinking about the future consequences of things.

It seems very optimistic and 90s to me now

Doesn't the added 0 suggest that it's abbreviated rather than not? E.g. 08 means 2008, so 02020 could be 32020?

Wouldn't it make more sense to use a better prefix such as Y2020 or CE2020? Or 0y2020?

Zero strikes me as the worst prefix to indicate it's not truncated. Since it has only ever been used to indicate truncation until now.

I thought apostrophes were used for truncation: `'08`?

Not always, and only in English.