Converge LP/MIP remote execution on the explicit-client pattern (remove remote-solve registry)

[ramakrishnap-nv]

Background

LP/MIP remote execution is triggered implicitly: solve_lp / solve_mip check is_remote_execution_enabled() (set by CUOPT_REMOTE_HOST / CUOPT_REMOTE_PORT) and reroute. Because that check lives inside cuopt_mathematical_optimization, the engine needs to call into cuopt_grpc — the reverse of the dependency direction, since cuopt_grpc already links the engine.

The workaround is a function-pointer registry: cuopt_mathematical_optimization holds nullable slots that libcuopt_grpc.so's ELF constructor fills via register_remote_solvers(), reached through a lazy dlopen. That lazy load is also why the slots have to be atomic — the constructor publishes them on whichever thread triggers the load while others may be reading.

Raised by @hlinsen in #1622:

The umbrella/CLI/Python layer should select local versus remote, with cuopt_grpc depending one-way on mathematical-optimization types. Can we remove the dlopen/atomic registration mechanism entirely?

The pattern already exists

#1597 (routing over gRPC) does this the clean way. Zero uses of CUOPT_REMOTE_HOST, is_remote_execution_enabled or get_memory_backend_type; no registry, no dlopen, no constructor registration. The user asks for remote explicitly:

client = RoutingClient("gpu-host:50051")
client.solve(data_model, settings)

cpu_routing_problem_t is a plain data type in cuopt_routing; the mapper, client and server live in cuopt_grpc. The dependency stays one-way and the routing engine stays local-only.

LP/MIP is the outlier, not the pattern.

Proposal

Add LPClient / MIPClient mirroring RoutingClient, then delete the registry:

• cpp/include/cuopt/mathematical_optimization/remote_solve_registry.hpp
• cpp/src/pdlp/remote_solve_registry.cpp
• cpp/src/grpc/client/grpc_registration.cpp
• the remote branches in cpp/src/pdlp/solve.cu, cpp/src/mip_heuristics/solve.cu, cpp/src/pdlp/utilities/cython_solve.cu and cpp/cuopt_cli.cpp

cuopt_mathematical_optimization becomes local-only and every component dependency is one-way. The dlopen, the atomics and the ELF constructor all go with it.

Open question

What happens to CUOPT_REMOTE_HOST / CUOPT_REMOTE_PORT. Keeping them as a deprecated compatibility path preserves existing users' setups; removing them is cleaner but is a user-visible break. This is a product decision, not a build one.

Sequencing

Depends on #1622 (component split) and #1597 (routing over gRPC). Best done in or right after #1597, which already owns the gRPC client layer and establishes the pattern — rather than in #1622, which would mean duplicating that design work and adding a user-visible API change to a build-focused PR.