Define `LinearSolverBackend` protocol and tighten operator contracts

[jc-macdonald]

Summary

Introduce the core backend protocol that all solver backends must satisfy.

Scope

Create src/op_engine/backends/__init__.py defining:

1. LinearSolverBackend(Protocol) — @runtime_checkable, with methods:

   • solve(left_op, right_op, x) -> NDArray — equivalent to current implicit_solve()
   • clear_cache() -> None — equivalent to clear_implicit_solver_cache()
   • convert_operator(op: OperatorLike) -> Any — replaces CoreSolver._as_scipy_operator()

2. Tighten OperatorLike — add dtype property (already checked in _SolverMeta but not in protocol)

3. Export LinearSolverBackend from op_engine.__init__

Files to create/modify

• src/op_engine/backends/__init__.py (new) — protocol definitions
• src/op_engine/__init__.py — add to exports

Acceptance criteria

• LinearSolverBackend is a typing.Protocol with @runtime_checkable
• mypy --strict passes for the new module
• No existing tests break (protocols are structural)

Dependencies

None — can start immediately.

Design context

Current anchor points in codebase:

• OperatorLike / PredictorLike protocols: core_solver.py ~L99-125
• ScipyOperator type alias: core_solver.py L149
• Operator / DenseOperator / SparseOperator aliases: matrix_ops.py L18-20