Can someone please explain how do the ETH1 balances become ETH2 if they don't move on-chain? How does eth1 become a shard? Is ETH2 an airdrop of eth1 balances?
ETH1 is a blockchain secured by Proof Of Work. ETH2 is a blockchain secured by Proof Of Stake.
Balance on ETH1 are reported on ETH2 so you have nothing to do, if you have 1 ETH on precedent network you will have 1 ETH on the newest.
But just as Bitcoin/Bitcoin cash, there is a risk that miners support a hard fork so you will end up with 1 ETH on PoS chain and 1 ETH on PoW chain legacy.
ETH1 does not become a shard, it becomes ETH2.
ETH2 is not technically an airdrop, your balance will be inchanged.