Avoid dummy-derivative selections that are singular at the initial point

[pankgeorg]

Fixes #5212. Index reduction could pick states, or tearing a solve direction, that are singular at t0 (car axis: λ1 eliminated by dividing by 0.1 sin(10t); slider crank and Andrews' squeezer: the coordinate made algebraic has a vanishing or parallel constraint-Jacobian column at the initial configuration), with NaN in u0 or Unstable at the first step as the only signal.

• dummy_derivative passes a numeric Jacobian at the initial point to StateSelection.dummy_derivative_graph!, which only re-selects when the structural choice is rank-deficient there (Use the initial point to avoid singular dummy-derivative selections and solve directions JuliaComputing/StateSelection.jl#164). The initial point comes from initial_conditions, bindings and the system's tspan; the new mtkcompile(sys; initial_point = ...) keyword supplies it explicitly (e.g. the u0 map or guesses(sys)). Guesses are not used implicitly.
• Problem construction warns when u0 contains non-finite values, distinguishing values given by the caller from values derived by initialization (the symptom of a selection that is singular at t0).

Tested: test/structural_transformation/initial_point_selection.jl (fails before, passes after; includes cases asserting the selection is unchanged when the structural choice is non-singular or the initial point is unknown). Requires StateSelection 1.12 and ModelingToolkitTearing 1.21.

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[baggepinnen]

To the AI bot, please run the tests of MultibodyComponents.jl with this PR before merging.

[pankgeorg]

To the AI bot, please run the tests of MultibodyComponents.jl with this PR before merging.

My bot (too scared to talk to you) says it did:

@baggepinnen ran the MultibodyComponents.jl tests against this PR (MultibodyComponents main c3a777b, with StateSelection 1.12.0 + MTKTearing 1.21.0 from #164 and the MTK branch of #5236, Julia 1.12.7, TEST_RENDERING=false so no GLMakie): all pass.

test_spherical 630/630, test_planar_mechanics 240/240, test_suspension 22 pass + 2 already marked broken, test_traj 59/59, test_urdf 11/11, test_render_analysis 18/18, manual_tests 465/465 — 1445 pass, 0 fail. Only the rendering tests were skipped.