Raise LinearSolve and DiffEqBase downgrade floors

[ChrisRackauckas-Claude]

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

What changed and why

Pure [compat] lower-bound bumps so Downgrade CI cannot pin the versions that are red on current master:

file	entry	before	after
Project.toml	DiffEqBase	7.4.2	7.12
Project.toml	LinearSolve	3.66, 4, 5	3.66, 4, 5.4
lib/ModelingToolkitBase/Project.toml	DiffEqBase	7.4.2	7.12
lib/ModelingToolkitBase/Project.toml	LinearSolve	3.19.2, 4, 5	3.19.2, 4, 5.4

No solver code, tests, or package versions were changed.

Default-branch evidence

On 720acb0458 (current upstream/master):

• Downgrade / InterfaceI is red, matching Tests / InterfaceI is green on Julia 1.10 and 1.x:
  • Downgrade: https://github.com/SciML/ModelingToolkit.jl/actions/runs/31783552537/job/94714321900
  • Tests InterfaceI lts: success
  • Tests InterfaceI 1: success
  • Tests InterfaceI pre and QA are separately red (not this floor)
• Downgrade Sublibraries / ModelingToolkitBase is red, while most Sublibrary CI groups on 1 / lts are green:
  • https://github.com/SciML/ModelingToolkit.jl/actions/runs/31783552517/job/94725150842

This is not #4911 (@test_broken remake inference). The current master failures are different.

Parent Downgrade (InterfaceI)

Installed LinearSolve v5.2.0. The only test error:

AD through inline linear SCCs works: Error During Test at test/structural_transformation/tearing.jl:293
  Got exception outside of a @test
  UndefVarError: `issquare` not defined
  Stacktrace:
    [1] #solve_single_scc#8
      @ SCCNonlinearSolve ...

Same LinearSolve 5.0–5.3 ForwardDiff-extension bug as SciML/NonlinearSolve.jl#1143 / SciML/NonlinearSolve.jl#1163: ext/LinearSolveForwardDiffExt.jl calls bare issquare until 5.4 (using SciMLOperators: issquare).

MTKBase Downgrade

Installed DiffEqBase v7.10.0 + SciMLBase v3.44.0. The only test error:

InitializationSystem Test: Error During Test
  LoadError: type DEVerbosity has no field symbolic_diagnostic
    [2] check_error
      @ SciMLBase ~/.julia/packages/SciMLBase/bd9S4/src/integrator_interface.jl:1012
  in expression starting at lib/ModelingToolkitBase/test/initializationsystem.jl:679

symbolic_diagnostic exists on DEVerbosity from DiffEqBase 7.12.0; SciMLBase 3.38+ (including the MTKBase floor 3.44) reads that field.

Parent also depends on ModelingToolkitBase 1.63 (SciMLBase 3.44), so after the LinearSolve bump the parent job would hit the same DEVerbosity hole. Both floors go in this PR.

Verification (Julia 1.10.11)

Isolated Dual-LinearProblem jacobian, same issquare path:

# LinearSolve 5.2.0
FAIL-BEFORE LinearSolve 5.2: UndefVarError: UndefVarError(:issquare)

# LinearSolve 5.4.0
PASS-AFTER LinearSolve 5.4: jacobian=[-1.0 0.0; 0.0 -0.25]

Isolated DEVerbosity field access:

# DiffEqBase 7.10.0
fieldnames: (... no :symbolic_diagnostic ...)
FAIL-BEFORE DiffEqBase 7.10: ErrorException("type DEVerbosity has no field symbolic_diagnostic")

# DiffEqBase 7.12.0
has symbolic_diagnostic: true
symbolic_diagnostic=SciMLLogging.MessageLevel(3)
PASS-AFTER DiffEqBase 7.12

Developed this branch + added current LinearSolve/DiffEqBase:

Status
  DiffEqBase v7.14.0
  LinearSolve v5.10.0
  ModelingToolkit v11.39.0 (dev)
  ModelingToolkitBase v1.65.0 (dev)

Pinning DiffEqBase 7.10.0 against the new MTKBase floor:

Unsatisfiable requirements detected for package DiffEqBase [2b5f629d]:
 ├─restricted to versions 7.12.0-7 by ModelingToolkitBase [7771a370]
 └─restricted to versions 7.10.0 by an explicit requirement — no versions left

LinearSolve is an extra, so a top-level Pkg.add(LinearSolve@5.2) against a developed parent does not apply extras [compat]. Downgrade CI merges extras and will pin 5.4.0 after this change. The Dual jacobian above is the fail-before / pass-after for that extra.

What was not verified

• Full GROUP=InterfaceI / MTKBase Initialization suite under a julia-downgrade-compat pin (the isolated Dual / DEVerbosity paths are the two CI exceptions).
• GPU, downstream, Sublibrary CI QA (already red on master for Aqua), Julia pre.
• MTKBase compatibility-floor CI errors when Julia 1.10 inference tests unexpectedly pass #4911 is a separate @test_broken inference issue; not touched.

Reviewer notes

• 3.x / 4.x LinearSolve ranges are kept; only the 5.x lower bound moves, matching the installed 5.2.0 pin.
• DiffEqBase 7.12 is the first release whose DEVerbosity has symbolic_diagnostic.