Add Fan Operating Mode select for active fan mode

[EdenNelson]

Add a fan_operating_mode select that exposes the purifier's active fan mode as a normal ESPHome select entity for dashboards that do not render fan presets directly.

Fixes #49

Summary

• Add type: fan_operating_mode to the Levoit select platform.
• Map select options to the existing raw MCU fan mode values used by the fan preset path.
• Expose model-specific fan operating mode options:
  • Core200S: Manual, Sleep
  • Core300S/Core400S/Core600S: Manual, Sleep, Auto
  • Vital100S/Vital200S: Manual, Sleep, Auto, Pet
  • Sprout: Manual, Auto
  • EverestAir: Manual, Sleep, Auto, Turbo
• Keep the new select synchronized from MCU status and local fan-control changes.
• Add the select to Levoit default device YAMLs and builder YAML mirrors.
• Document that Fan Operating Mode is the active fan mode and is distinct from Auto Mode / Auto Profile.

Validation

• git diff --check passed.
• Editor diagnostics reported no errors in the Python/select code; C++ diagnostics only showed local include-path noise for ESPHome headers.
• ESPHome Core400S local compile passed with fan_operating_mode configured.
• Live YAML config validation passed against EdenNelson/levoit@integration/core400s-auto-profile-stack.
• Core400S live testing passed: ESPHome Web UI shows the Fan Operating Mode select, and the dropdown updates to Manual when fan operation changes.

Scope

This PR exposes the active fan operating mode through a normal ESPHome select while keeping existing fan preset behavior intact. It does not add remembered Room Size persistence, Manual/Auto mechanics changes, Core room-size encoding changes, diagnostics, raw sensors, generated YAML churn beyond required config mirrors, or unrelated model behavior changes.

Disclosure

This PR was prepared with GitHub Copilot/AI assistance and human-in-the-loop review. Live validation was performed by a human on a Core400S using air-purifier-office.yaml. Other model option sets mirror the existing fan preset mode support and were not hardware-tested.

[tuct]

Hi,
Could you check the merge conflict @EdenNelson ?
And thank you for your contributions!!!

[EdenNelson]

Fixed and tested. Thank you.