[FLINK-33678][streaming-java] Remove StateBackend related public API.

[JunRuiLee]

What is the purpose of the change

[FLINK-33678][streaming-java] Remove StateBackend related public API.

Verifying this change

This change is a trivial rework / code cleanup without any test coverage.

Does this pull request potentially affect one of the following parts:

• Dependencies (does it add or upgrade a dependency): (yes / no)
• The public API, i.e., is any changed class annotated with @Public(Evolving): (yes / no)
• The serializers: (yes / no / don't know)
• The runtime per-record code paths (performance sensitive): (yes / no / don't know)
• Anything that affects deployment or recovery: JobManager (and its components), Checkpointing, Kubernetes/Yarn, ZooKeeper: (yes / no / don't know)
• The S3 file system connector: (yes / no / don't know)

Documentation

• Does this pull request introduce a new feature? (yes / no)
• If yes, how is the feature documented? (not applicable / docs / JavaDocs / not documented)

[flinkbot]

CI report:

• d1ef0ed Azure: SUCCESS

Bot commands

The @flinkbot bot supports the following commands:

• @flinkbot run azure re-run the last Azure build