Drop KrylovPreconditioners from Core tests

[ChrisRackauckas-Claude]

Please ignore this PR until it has been reviewed by @ChrisRackauckas.

Summary

• Replace the external BlockJacobiPreconditioner used by the Core tests with a public-API LinearAlgebra inverse diagonal preconditioner.
• Remove the test-only KrylovPreconditioners compat, extra, target, and import entries.
• Remove LinearSolve's package-specific no_promote override from the downgrade workflow.

Root cause and impact

KrylovPreconditioners was used indirectly through its exported BlockJacobiPreconditioner name, but its historical Arpack/LightGraphs dependency graph cannot be minimum-resolved with the rest of LinearSolve's test environment. PR #1091 worked around that resolver conflict by excluding the package from minimum promotion.

The existing tests only require an inverse-like preconditioner to exercise the Krylov wrapper. Diagonal(inv.(diag(A))) provides that behavior using public LinearAlgebra APIs. The GMRES and FGMRES preconditioned cases retain ldiv = false, so the inverse-preconditioner multiplication path remains covered. The (M, I) tuple continues to cover a nontrivial left preconditioner and identity right preconditioner, and the existing counting factory still verifies reuse_precs = true without rebuilding the preconditioner.

This changes only test infrastructure and downgrade coverage; it does not change LinearSolve's runtime dependencies or public API.

Process

The requested task was to replace the downgrade promotion exception with a focused dependency fix without skipping or weakening tests. I reviewed current main, #1091, and the history that introduced the preconditioner tests. That review showed the dependency was used indirectly through an exported symbol, so I preserved the solver and reuse coverage with the documented stdlib preconditioner interface instead of deleting those cases. I then ran the exact downgrade resolver, locked downgrade and current Core suites, formatting, workflow, TOML, and diff checks before committing.

Local validation

• Ran the Julia 1.10 julia-actions/julia-downgrade-compat v2.6.1 resolver in deps mode with the reusable workflow's default Mooncake exclusion. Resolution completed successfully, and the resulting manifest did not contain KrylovPreconditioners.
• Ran Pkg.build() against the downgraded manifest successfully.
• Ran GROUP=Core on Julia 1.10 with force_latest_compatible_version = false and allow_reresolve = false: the full Core suite passed; Basic Tests passed 590/590.
• Built the current Julia 1.12 environment and ran the same strict GROUP=Core command: the full Core suite passed; Basic Tests passed 590/590.
• Ran Runic over the full repository: 142/142 Julia files passed.
• Ran actionlint .github/workflows/Downgrade.yml, parsed and checked the Project.toml test target declarations, and ran git diff --check; all passed.

Prior art

This replaces the package-specific workaround merged in #1091 with a dependency-level fix while preserving the affected preconditioner behavior tests.

[ChrisRackauckas-Claude]

CI triage: the downgrade job passed. The three failing jobs are exact clean-base failures from base SHA 0496f135 and are unrelated to this branch: both Julia 1 and Julia LTS AD jobs report the same Static Arrays inferred-return-type mismatch, and the NonlinearSolve downstream job reports the same Generalized Rosenbrock failure plus Brown-almost-linear unexpected pass. Base evidence: AD Julia 1, AD Julia LTS, NonlinearSolve downstream. No branch change is warranted for these failures.