Use live parameters in sparse constraint Jacobians

[ChrisRackauckas-Claude]

Important

Ignore this PR until it has been reviewed by @ChrisRackauckas.

Summary

• accept the live parameter argument in generated and analytic sparse constraint-Jacobian callbacks
• rebuild DifferentiationInterface preparation when the live state or parameter type changes
• cover in-place/out-of-place and generated/analytic callbacks directly in OptimizationBase
• exercise generated and analytic sparse callbacks through OptimizationIpopt

Root cause

OptimizationIpopt switched to the generic OptimizationCache in #1257. That cache invokes constraint Jacobians with the current parameter value. The sparse instantiation path still produced two-argument callbacks that captured the initial parameter, causing a MethodError when called as cons_j(J, x, p). The out-of-place path had the equivalent missing live-parameter behavior.

This patch preserves the old two-argument convenience through default arguments while making the current parameter part of differentiation and analytic callback evaluation.

Investigation

• reproduced the failure from current master at be6fbd279
• traced the behavior change to Use the default OptimizationCache in OptimizationIpopt #1257; the same BoundaryValueDiffEq case passed with OptimizationIpopt 1.2.3
• reduced it to sparse generated and analytic constraint Jacobians
• added direct four-way coverage in OptimizationBase and an in-place solver integration test in OptimizationIpopt

Local validation

• OptimizationBase AD: 729 passed
• OptimizationIpopt Core: 129 passed, 1 pre-existing broken
• Runic check passed for all three changed Julia files
• git diff --check passed