Distributed Linear Solvers in LinearSolve.jl

This project will add distributed linear solver support to LinearSolve.jl by expanding and hardening PETSc.jl integration. The goal is to let SciML users solve large-scale systems (Ax=b) on HPC clusters through the same high-level LinearSolve API they already use for local solvers. The work will focus on implementing and improving PETSc-based KSP wrappers, cache-aware re-solve workflows, preconditioner configuration, and distributed matrix/vector support with MPI. It will also include tests, benchmarks, and documentation so users can reliably switch between direct, iterative, and distributed methods without changing downstream solver code.