No, it is not. If the server accepts the hash from an untrusted source (the client), then that's equivalent to not using hashes at all. The reason why we hash is so a database leak does not allow malicious actors to login directly. If the server accepts a hash, that means it only does hash_from_client == hash_from_db, meaning that's the same as doing password_from_client == password_from_db in terms of security. This is because the client can just send the hash from the DB, the user does not actually need to know the password, hence your proposal is equivalent to not using hashes at all in terms of security.

The point of sending hashes info from the client is that each site uses a different key, even if publicly available. This means that leaked login data cannot be compared or matched across different leaks.

That is for keyed hash functions, which is not typically done for passwords (but peppers are sometimes used, which helps similarly). This does not prevent the above scenario, though, because the leaked hash can still be used on that site. Sending hashes is a bad idea, the hash should always be computed in a trusted environment to ensure the user actually knows the password.