Fix Downgrade CI: bump NonlinearSolve (4.12) and OrdinaryDiffEqSDIRK (1.7) floors

[ChrisRackauckas-Claude]

Problem

The Downgrade / Downgrade Tests job on master is red — it fails during precompilation.

Root cause (three interlocking stale-floor incompatibilities)

The old test-dep compat floors make the SciML reusable downgrade workflow (Resolver.jl
--min=@deps) resolve a stale, mutually-inconsistent valley of versions that trips three distinct
precompile failures. Each floor bump removes one:

1. NonlinearSolve v3 + new DiffEqBase. v3 does
   using DiffEqBase: AbstractNonlinearTerminationMode, but that type was moved out of DiffEqBase
   into NonlinearSolveBase. v3's DiffEqBase compat is under-bounded (6.149.0, no upper cap),
   so the resolver pairs it with DiffEqBase v6.174.0 which no longer defines it:
   UndefVarError: AbstractNonlinearTerminationMode not defined.

2. NonlinearSolve 4.0.x + NonlinearSolveBase 1.5.x. Both define the same
   SciMLBase.__solve(::DualAbstractNonlinearProblem, alg, ...) (NonlinearSolve's forward_diff.jl
   and NonlinearSolveBase's ForwardDiff ext): Method overwriting is not permitted during Module precompilation.

3. OrdinaryDiffEqSDIRK 1.2.0 + new OrdinaryDiffEqDifferentiation. SDIRK 1.2.0 builds TRBDF2
   with a legacy tuple AD field (AutoForwardDiff, Val{0}, Val{:forward}) that the resolved
   OrdinaryDiffEqDifferentiation 1.16's prepare_ADType no longer accepts, so PDESystemLibrary's
   top-level solve(prob, TRBDF2()) in lib/brusselator.jl dies at precompile with a
   prepare_ADType MethodError.

Fix

-NonlinearSolve = "3, 4"
+NonlinearSolve = "4.12"
-OrdinaryDiffEqSDIRK = "1.2.0, 2"
+OrdinaryDiffEqSDIRK = "1.7, 2"

• NonlinearSolve 4.12 is the first 4.x requiring NonlinearSolveBase = "2" (where __solve
  lives in exactly one place) — kills (1) and (2).
• OrdinaryDiffEqSDIRK 1.7 is the first version carrying an
  OrdinaryDiffEqDifferentiation = "1.12 - 1" compat (the modern AD API) — kills (3).

With these floors the downgrade resolves a consistent set:

package	resolved (downgrade)
NonlinearSolve	4.12.0
NonlinearSolveBase	2.2.0
OrdinaryDiffEqSDIRK	1.7.0
OrdinaryDiffEqDifferentiation	1.16.1
OrdinaryDiffEq	6.97.0
DiffEqBase	6.202.0
ModelingToolkit	9.50.0
SciMLBase	2.116.0

The non-downgrade builds already resolve NonlinearSolve 4.19.x and SDIRK 2.7.x, so these floor bumps
have no effect on them.

Local verification (Julia 1.10.11)

Reproduced the exact CI downgrade by running the real julia-actions/julia-downgrade-compat
downgrade.jl (mode=deps, Resolver.jl --min=@deps) against the patched Project.toml, then
precompiling the resolved environment. Result: 0 packages failed (✗), and none of the three
errors above appear. Critically, PDESystemLibrary itself precompiled ✓ — its top-level
solve(prob, TRBDF2()) (the call that previously threw the prepare_ADType MethodError) now runs
clean, as do NonlinearSolve / NonlinearSolveBase / OrdinaryDiffEqNonlinearSolve / OrdinaryDiffEqSDIRK.

Please ignore until reviewed by @ChrisRackauckas.

🤖 Generated with Claude Code