[FLINK-37001][table] Remove code related to registerTableSinkInternal in tests and remove this method in TableEnvironmentInternal

[xuyangzhong]

What is the purpose of the change

Remove all direct uses of TableEnvironmentInternal#registerTableSinkInternal in table module.

Brief change log

• Remove all direct uses of TableEnvironmentInternal#registerTableSinkInternal in table module
• Remove the method TableEnvironmentInternal#registerTableSinkInternal

Verifying this change

This change is already covered by existing tests.

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

• Dependencies (does it add or upgrade a dependency): no
• The public API, i.e., is any changed class annotated with @Public(Evolving): no
• The serializers: no
• The runtime per-record code paths (performance sensitive): no
• Anything that affects deployment or recovery: JobManager (and its components), Checkpointing, Kubernetes/Yarn, ZooKeeper: no
• The S3 file system connector: no

Documentation

• Does this pull request introduce a new feature? no
• If yes, how is the feature documented?

[flinkbot]

CI report:

• 2ebe54f Azure: SUCCESS

Bot commands

The @flinkbot bot supports the following commands:

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

[lsyldliu]

@xuyangzhong Thanks for your contribution, I left some comments.

[xuyangzhong]

@flinkbot run azure

[xuyangzhong]

@flinkbot run azure

[xuyangzhong]

@flinkbot run azure

[lsyldliu]

LGTM