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Co-authored-by: QuantumGhost <obelisk.reg+git@gmail.com>

refactor(api): Separate SegmentType for Integer/Float to Enable Pydantic Serialization (#22025)

This PR addresses serialization issues in the VariablePool model by separating the `value_type` tags for `IntegerSegment`/`FloatSegment` and `IntegerVariable`/`FloatVariable`. Previously, both Integer and Float types shared the same `SegmentType.NUMBER` tag, causing conflicts during serialization.

Key changes:
- Introduce distinct `value_type` tags for Integer and Float segments/variables
- Add `VariableUnion` and `SegmentUnion` types for proper type discrimination
- Leverage Pydantic's discriminated union feature for seamless serialization/deserialization
- Enable accurate serialization of data structures containing these types

Closes #22024.

Co-authored-by: Novice <novice12185727@gmail.com>

This pull request introduces a feature aimed at improving the debugging experience during workflow editing. With the addition of variable persistence, the system will automatically retain the output variables from previously executed nodes. These persisted variables can then be reused when debugging subsequent nodes, eliminating the need for repetitive manual input.

By streamlining this aspect of the workflow, the feature minimizes user errors and significantly reduces debugging effort, offering a smoother and more efficient experience.

Key highlights of this change:

- Automatic persistence of output variables for executed nodes.
- Reuse of persisted variables to simplify input steps for nodes requiring them (e.g., `code`, `template`, `variable_assigner`).
- Enhanced debugging experience with reduced friction.

Closes #19735.

- Extract methods used by `ParameterExtractorNode` from `LLMNode` into a separate file.
- Convert `ParameterExtractorNode` into a subclass of `BaseNode`.
- Refactor code referencing the extracted methods to ensure functionality and clarity.
- Fixes the issue that `ParameterExtractorNode` returns error when executed.
- Fix relevant test cases.

Closes #20840.

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