I’ve looked into this a bit myself, and unfortunately, Bitcoin doesn’t have a straightforward way to unlock funds automatically without some sort of extra action. Most time-lock solutions, like HTLCs or nLockTime, still need you to make a move when the time’s up.
No, that's incorrect. Please read my previous answer.You don't have to "make a move when the time is up" with CLTV/CSV. When the time is up, you (or the recipient of the payment) can spend the coins normally.
Of course you have to spend them, e.g. buying something or deposit the coins to an exchange. But in the case of Ethereum, you have to spend them too after they "unlock".
You may instead refer to an automatic payment after the unlock. But that was not what the OP requested afaik. It would also not make much sense: If you should be able to retract (spend to another address) before the locktime ends, then you can simply use nLocktime. If not (i.e. if your goal is that the funds will be paid without mattering what happens) then you can make either an upfront payment or use CLTV/CSV to avoid the recipient spends the coins before the lock.
