Refactor IntermediateTIState enum across Airflow components

### Description

- Move IntermediateTIState enum from airflow.utils.state to right location
- Update all imports in airflow-core to use the new IntermediateTIState location
- Add deprecation warning in airflow.utils.init.py for backward compatibility

### Use case/motivation

_No response_

### Related issues

https://github.com/apache/airflow/issues/53385
https://github.com/apache/airflow/issues/51671

### Are you willing to submit a PR?

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

### Code of Conduct

- [x] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

Start by locating IntermediateTIState in airflow.utils.state and review the related issues #53385 and #51671 to determine its intended new location. Update the airflow-core imports and add the backward-compatibility deprecation handling in airflow.utils.init.py; the work is done when all specified imports use the new location without breaking the old one.

Written by the indexing model from the issue text.