Split search finish finalization module

[yvette-carlisle]

Summary

• Move ElfService::finish_search from search/service.rs into the search::finish owner module.
• Keep the method scoped to crate::search so search/service.rs and search/retrieval/flow.rs can call it without widening it to a crate-wide API.
• Leave raw search orchestration in search/service.rs.

Validation

• cargo make fmt-rust
• cargo make check-rust
• cargo make lint-vstyle
• cargo make lint-rust
• cargo make test-rust
• cargo make check
• cargo make test-rust-integration
• cargo make check-trace-gate
• git diff --cached --check