Always mount subscription router (demo-safe) and prevent duplicate router mounts

[AJaySi]

Motivation

• Ensure api.subscription endpoints (payment/preflight/subscription) are always available regardless of demo or special modes.
• Avoid double-registration of the same router which can cause duplicate routes or inclusion errors when core and safety-net paths both run.
• Preserve existing middleware behavior (API key injection, rate limiting, monitoring) so subscription-related middleware remains active in demo mode.

Description

• Add _included_router_names tracking to RouterManager and make include_router_safely skip already-included routers to prevent duplicates.
• Make subscription router an explicit first-class include inside RouterManager.include_core_routers so it is mounted even in demo scenarios.
• Add a safety-net call to router_manager.include_router_safely(subscription_router, "subscription") in both backend/app.py and backend/main.py to guarantee subscription routes remain mounted if core inclusion changes.
• Add lightweight logging for demo_mode in RouterManager while leaving middleware registration/order unchanged.

Testing

• Ran python -m py_compile backend/alwrity_utils/router_manager.py backend/app.py backend/main.py, which completed successfully.

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Codex Task