Medium: [DynamicExtraction] Define stage-wise distribution coefficient handling

[Mazhar331]

Follow-up from #120 / #56

PR #120 fixes #56 by supplying a default DynamicExtractor.k_fun and validating activity-model selectors. While addressing review feedback on that PR, an inline TODO in DynamicExtraction.py surfaced a separate limitation: the dynamic extractor currently does not define or validate stage-wise K_i callback semantics.

Problem

DynamicExtractor.material_balances and the initialize_model equilibrium correction both call self.k_fun(...) and then use the returned K_i values across staged algebra. The current code comments note that stage-wise handling is not implemented. That is broader than the #56 regression, which only ensures the default callback exists and returns dimensionless K_i = gamma_light/gamma_heavy.

Without an explicit stage-wise callback contract, future changes can silently rely on broadcasting or shape coincidences instead of intentional (num_stages, num_comp) behavior.

Scope

• Define the accepted k_fun return shapes for scalar, component-wise, and stage-wise distribution coefficients K_i [-].
• Update DynamicExtractor.material_balances and the initialize_model equilibrium correction to validate or broadcast those shapes deliberately.
• Add tests with unequal numbers of stages and components so stage/component broadcasting mistakes cannot stay green.
• Include units/docs/comments coverage for mole fractions [-], temperature [K], activity coefficients [-], and distribution coefficients K_i [-].

References

• Deferral source: Fix DynamicExtractor default equilibrium function #120
• Original fixed bug scope: High: [DynamicExtraction] DynamicExtractor default constructor leaves k_fun undefined #56