"What happened to the private keys" is only an interesting question if we know something happened to them at all.
For all anyone knows, Satoshi is a government biding its time, aliens, a hacker with a messy apartment, dead and their inheritors don't know what they have, already independently wealthy and doesn't care about their wallet, did it all for the lulz and doesn't care about the wallet. It's apparently not, but if this were Satoshi then I find these questions far more interesting: Who is Satoshi? Why was their identity hidden? Why emerge now?
Satoshi was probably Hal Finney, who passed away in 2014. The most likely explanation of what happened to the keys is that they weren’t properly safe guarded early in development because no one thought that one day bitcoins would be worth $20,000 a piece. When Finney died their total value was “only” around $45 million.
If Satoshi is Hal Finney, and dead, then "what happened to the keys" isn't an interesting question. If this were Satoshi reemerging, then "what happened to the keys" isn't relevant, because they're clearly fine.
Quite the opposite. If Satoshi is still alive that entity is worth around $10 billion. Incentives are a powerful thing and the fact that Satoshi hasn’t made a transaction in years is strong evidence those keys are lost.
My blockchain might be a little rusty, but is it possible to tell the order in which a coin was mined (vs the total) from the information in the chain?
If so, should be possible to find satoshi coins relatively easily, no?
Bitcoin doesn’t really work like that, a “coin” is just a value tied to an address, so individual coins are never transferred. What you can do is see all the incoming transactions to an address to identify which addresses received the earliest mined coins.