[Umbrella] Flink Engine Improvement and Quality Assurance

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://www.apache.org/foundation/policies/conduct)

### Search before asking

- [X] I have searched in the [issues](https://github.com/apache/incubator-kyuubi/issues) and found no similar issues.

### Describe the proposal

We introduced the Flink engine in https://github.com/apache/incubator-kyuubi/issues/1322.

In this ticket, we collect feedback, improvements, bugfixes, aim to make it production-ready

### Task list

### Bugs

### Improvement
- [x] #2002 @link3280
- [ ] #1652 @yanghua
- [ ] #1865 @SteNicholas
- [ ] #2159 @deadwind4
- [x] #2405
- [ ] #2252

### Documentations

### Brainstorming

### Miscs

### Are you willing to submit PR?

- [ ] Yes I am willing to submit a PR!

Start by reading the unchecked task issues #1652, #1865, #2159, and #2252, along with the completed items for context. The umbrella issue provides no specific files or tests; done would require resolving the listed Flink-engine improvements, bugs, and documentation needs until the engine is production-ready.

Written by the indexing model from the issue text.