Ah okay, but can a contract stake the ada which was sent into a contract?

It's not exactly, how I would describe it. A contracts has an address. ADA and other token sent to a contract are sent to these addresses. And a contract transaction can take outputs that are currently at these addresses

The address of a contract can contain a stake address. And then, the ADA waiting at this contract are delegated to the pool selected for this stake address. But it's not really an action of the contract to stake, unstake, stake somewhere else. It's something build on the infrastructure the contract is running on.