Does the hash of an Ethereum block changes every time I deploy a contract on it?

Noob question yet again and apologies in advance. So my understanding till now is that each Ethereum block can hold a fixed number of smart contracts and every time I deploy a contract on the block, its hash will change.

Now because of that, for each deployment, the hashes of all the succeeding blocks will have to be calculated yet again, which of course should not be the case. So I think I am misunderstanding something here.

Is it that deploying a contract on the chain does not change the hash of the block? How does it actually work?