One way to do it: remove the old derivative outputs, local solvers and deprecated declarations #235

Part of #237.

Why

After #221 there are two ways to do most things:

Two paths double the tests and the documentation. They also leave material authors unsure which path is current.

Design (in this order; each step is its own PR)

1. Hosts read derivatives.
   • The UMAT DDSDDE (and DDSDDT from Migrate materials to declared partials and residual systems #219) come from derivative(stress, strain);
   • the report tool's tangent check uses derivative();
   • the FFT homogenization adapter does the same (a PR in that repo).
2. Deprecate the old outputs with [[deprecated]] accessors for one tagged release. Each material keeps computing them only while a host still reads them.
3. Remove them. The hand-written tangents survive only as test references (moved into tests/), so the 1e-12 comparisons keep an independent reference.
4. Remove the local solvers. vector_newton and backward_euler are first wrappers over system (part of Migrate materials to declared partials and residual systems #219), then deprecated, then removed. The same applies to residual_source.
5. Remove the deprecated declaration API #190: remove the deprecated declaration API once numsim_material target: emit add_callback(...).reads(...) instead of the deprecated add_output callback numsim-codegen#161 has landed.

Tests

• Every test that read an old output reads the derivative instead, or moves to the test reference.
• The report CSVs are byte-identical, since the tangent check now comes from derivative().
• grep -rn "deprecated" include/ is empty at the end.

Depends on

• The rest of Migrate materials to declared partials and residual systems #219 (J2/Drucker–Prager/kinematic on system, DDSDDT)
• numsim_material target: emit add_callback(...).reads(...) instead of the deprecated add_output callback numsim-codegen#161 for step 5
• The numsim-fft-homogenization adapter switching to derivative()

Out of scope

Second derivatives (isotropic_damage keeps its split callbacks).