[rush reporter][R6] Add install-run-rush bootstrap handoff and compatibility adapters

[TheLarkInn]

Parent: #5858

Blocked by: #5974, #5975

Goal

Extend reporter ownership to startup/version-selection output without destabilizing the existing bootstrap script.

Scope

• Decide and implement the safest bootstrap shape: a reporter-aware install-run-rush variant, as suggested in [rush] Rush Reporter Overhaul #5858, or a backward-compatible prelude in the existing script.
• Parse only early reporter controls in the zero-dependency bootstrap.
• Buffer bounded Rush-owned startup envelopes, preserve inherited npm output as raw external output, and publish a nonce-protected handoff path via private environment variables.
• Replay and delete the handoff in the frontend host; clean abandoned files.
• Add new-frontend/old-engine and old-frontend/new-engine compatibility adapters with legacy-visible fallback.

Acceptance criteria

• Direct rush and bootstrap-mediated invocation converge on one authoritative frontend manager.
• Handoff replay/deletion, truncation, overflow, permissions, and cleanup behavior match RFC §5.5.
• Unsupported explicit requests fail; automatic/implicit selection falls back safely.
• Old global/new local and new global/old local combinations retain usable legacy output.
• Existing bootstrap consumers are not forced onto the new visible reporter path.

DAG

Unblocks R9 and completes startup ownership; it is intentionally not on the shortest direct-invocation demo path.

Part of #5858.