Allow LinearSolve 5 across implicit solver packages

[ChrisRackauckas-Claude]

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

Summary

• Allow LinearSolve 5 across the OrdinaryDiffEq implicit-solver subpackages that currently accept LinearSolve 3/4.
• Bump each affected subpackage patch version.
• Exercise LinearSolve 5 in the sparse-differentiation and ModelingToolkit test environments.

This is the OrdinaryDiffEq companion to SciML/ExponentialUtilities.jl#257 and is required by NonlinearSolve 4.23, whose current dependency graph resolves LinearSolve 5.

Local verification

• On the dependent Reuse homotopy caches across implicit ODE stages #3985 stack, ODEDIFFEQ_TEST_GROUP=Core julia +1.12 --startup-file=no --project=lib/OrdinaryDiffEqNonlinearSolve -e 'using Pkg; Pkg.test()' resolved LinearSolve 5.0.1 and exited 0.
• The complete Core run passed all functional sections, including Linear Solver Tests 113/113, Split ODE Tests 10/10, Mass Matrix Tests 225 passed with 42 existing broken, Sparse Jacobian Tests 11/11, and Matrix-Free WOperator Tests 14/14.
• Whole-repository Runic --check and git diff --check exited 0.

The homotopy cache work tested in the same local stack is kept in the separate follow-up #3985.

[ChrisRackauckas-Claude]

CI checkpoint: the root Downgrade / InterfaceI failure is the existing resolver-floor baseline tracked by #3917 and SciML/.github#118. The workflow pins SciMLOperators 1.15.0 explicitly, while stacked prerequisite #3983 correctly restores the OrdinaryDiffEqDifferentiation floor to 1.24.4, so resolution stops before tests run.

This same prerequisite baseline is already present on #3983; it is unrelated to the LinearSolve 5 compatibility changes in this PR. I am leaving the test and compatibility floors intact rather than weakening or bypassing them.

[ChrisRackauckas-Claude]

Clean-rebase update: this branch now contains only the LinearSolve 5 compatibility commit directly on current master; it no longer includes or depends on #3983.

The early GlobalDiffEq and OrdinaryDiffEqRosenbrock downgrade resolution failures reproduce on untouched master at 8fc48e69. They were introduced by the monorepo path-source changes in af88f3d and 79dcf13, respectively. The resolver-side correction is tracked in julia-actions/julia-downgrade-compat#56. Testing that correction locally exposed four later minimum-compatible Rosenbrock/AutoEnzyme failures, now tracked in #3987.

On the dependent #3985 stack, the official OrdinaryDiffEqNonlinearSolve Core group resolved LinearSolve 5.0.1 and exited 0; whole-repository Runic and git diff --check also exited 0.