With DSE Cassandra 5.x, in the client code is cassandra-driver-core to be excluded from dependency due to deprecation? Is dse-java-driver-core to be used instead?
I'm not 100% sure on what you're referring, I think that the primary reason is rework of the authentication support, and other things that are specific to DSE driver. OSS driver supports only username/password authentication, while DSE driver also supports Kerberos, plus mixed internal/external authentication schemas.
But you can safely replace cassandra-driver-core with dse-java-driver-core - code is compatible, the same Cluster/Session, only if you don't need geo types, graph support, etc. Look here for full list of differences.