Avoid non-public promote_op in OptimizationBase

[ChrisRackauckas-Claude]

This PR should be ignored until reviewed by @ChrisRackauckas.

Summary

• Replace the Base.promote_op dependency in OptimizationDIExt.jl with a local public-API output-eltype helper.
• Keep the p-accepting constraint Jacobian output buffer usable for dual and numeric parameter eltypes.

Root cause

OptimizationBase QA on master failed ExplicitImports.all_qualified_accesses_are_public because Base.promote_op is not public API.

Verification

Reproduced on the pre-fix base (59bdb75fe):

• OPTIMIZATION_TEST_GROUP=QA julia --project=lib/OptimizationBase -e 'import Pkg; Pkg.test()'
• Result: NonPublicQualifiedAccessException: promote_op is not public in Base; summary 16 passed, 1 errored, 1 broken.

Verified on this rebased branch (5cb560a08940f5592cd79b1654544afc6961d2f1):

• timeout 3600 env JULIA_DEPOT_PATH=/home/crackauc/sandbox/tmp_20260708_165240_11300/Optimization.jl/.julia-depot OPTIMIZATION_TEST_GROUP=QA julia --startup-file=no --project=lib/OptimizationBase -e 'import Pkg; Pkg.test(; coverage=false, julia_args=["--check-bounds=auto", "--compiled-modules=yes", "--depwarn=yes"], force_latest_compatible_version=false, allow_reresolve=true)'
  • Result: Quality Assurance | 17 pass, 1 broken, 18 total; Testing OptimizationBase tests passed.
• timeout 3600 env JULIA_DEPOT_PATH=/home/crackauc/sandbox/tmp_20260708_165240_11300/.julia-depot julia --startup-file=no --project=/home/crackauc/sandbox/tmp_20260708_165240_11300/.runic-env -m Runic --check lib/OptimizationBase/src/OptimizationDIExt.jl
  • Result: passed.
• git diff --check origin/master..HEAD
  • Result: passed with no output.

[ChrisRackauckas]

Do an ignore/allow on promote_op here and use it.

[ChrisRackauckas-Claude]

Current downstream status from the regression sweep:

• The direct OptimizationBase QA failure here is fixed by this PR (Base.promote_op public-API access).
• Downgrade-sublibraries failures are handled separately in Fix downgrade sublibrary bounds #1252.
• NeuralPDE GROUP=NNPDE dispatch failure is handled in Alias legacy NNPDE test group NeuralPDE.jl#1084.
• The MTK initialization/ForwardDiff dual hashcons failure is now split correctly: Handle throwing scalar equality in hashconsing JuliaSymbolics/SymbolicUtils.jl#1005 fixes the hashconsing invariant, and Add ForwardDiff dual initialization regression test ModelingToolkit.jl#4716 carries the MTK regression test.
• A separate current NeuralPDE master GROUP=NNODE numerical failure is under investigation in a separate worker.