refactor: centralize provider mode helper for host integrations

[rlippmann]

What changed

• Introduced a shared host-side provider helper at host_support/provider_mode.py for strict provider mode resolution and one-time startup logging.
• Refactored LiteLLM integration examples and demo LLM client to use the shared helper, preserving existing provider-mode behavior.
• Kept numbered examples non-package style by restoring local _util imports and removing examples/init.py.
• Updated tests to cover shared helper behavior and adjusted integration/demo tests to use the new helper import path.
• Updated wheel packaging to include host_support so integrations and demos can import the shared helper from built artifacts.

Why this was needed

• Avoid duplicated provider-resolution logic across examples and demos.
• Keep host/integration concerns out of engine code while still avoiding examples package coupling.
• Ensure packaged wheels contain both examples/... and host_support/provider_mode.py for runtime parity.