When validators stake ETH after the merge, would that ETH be beholden to the same hard-fork to that allows pre-merge staked ETH to be withdrawn?
example: post merge, stake ETH. what is the withdrawal process?
I don't think the withdrawal process has been fully decided. But I don't see any reason to treat any stakers differently: everyone can withdraw at the same time.
Most likely the process will be really straightforward: a contract is created which enables the withdrawal and anyone who wants to, can unstake and withdraw their Eth. This of course stops your possible node operations if the stake is being used for running a validator node.
We may not be that far away from the merge but there we are some time away from when withdraws are activated, meaning, this is all subject to change.
After withdrawals have been activated, validators can signal to the network that they wish to stop preforming any duties by submitting a voluntary exit transaction to the beacon chain. Any validators that has been active for for 256 epochs (~27 hours) can initiate a voluntary exit.
It takes at a minimum 5 epochs (32 minutes) for a validator to exit after initiating a voluntary exit. This number can be much higher depending on how many other validators are queued to exit.
Even though users can perform a voluntary exit in phase 0, they cannot withdraw their exited funds at this point in time. This implies that the staked funds are effectively frozen until withdrawals are enabled in future phases.
Staking ETH after the Merge is going to be the same as staking ETH before the Merge. They will follow the same process for deposit, the same process for validators and the same process for withdrawal. I explained the withdrawal process in Withdrawal activation through a hard fork and the role of the Eth2 Deposit Contract post-Merge if you want to learn more about it.