[singhharsh1708]

This cuts the fixed cost of a solve with a sparse jac_prototype. The Jacobian's rows are kept as one flat CSR that the AIJ matrix is built from directly, so filling the matrix is a single copy, and the colouring of a pattern is computed once and shared by later solves on the same pattern; only the read-only colouring result is shared, while DifferentiationInterface's buffers are still built per solve.

Results are bitwise identical to main on 18 solve paths (sparse AD and user Jacobians, sparse and diagonal mass, DAE, TSIRK, finite differences, TSAlpha2), with PETSc.jl 0.4.14 and 0.5.3, and the new rows equal the old nested rows on 5000 random patterns. On the 1-D Brusselator (n = 1000) setup goes from 204 to 96 µs and a one-step TSRosW solve from 342 to 235 µs with 937 allocations instead of 7041; on the 2-D Brusselator (n = 2048) setup goes from 470 to 179 µs and a one-step TSRosW solve from 867 to 547 µs (Julia 1.12, PETSc 3.22, minima of interleaved runs).

AI Disclosure: Claude assisted with the code. Testing and review by @singhharsh1708.