Support differentiation through LM solver

[chungmin99]

This PR adds a differentiable solver API, and demonstrates it in an end-to-end IMU fusion calibration example (Full-LM vs Deep-LM).

• Introduces solve_differentiable() with implicit/adjoint gradients through the inner LM solve,
• New differentiable solve path using custom_vjp and one adjoint linear solve (conjugate_gradient or dense_cholesky).
• Proper tangent/cotangent handling for manifold variables in backprop through the solve.
• A full sensor-calibration example with outer-loop bias learning via Optax and trajectory/bias comparisons.