feat(omni-agent): agentMode structure update; add game mode support

[cjraft]

Summary

restructuring the AgentMode type and adding support for a new "game" mode.

Key Changes:

• AgentMode Structure: Changed AgentMode from a simple string union type to an object structure with id, link, and browserMode properties
• New Game Mode: Added support for "game" mode with specialized prompts and behavior

Checklist

• Added or updated necessary tests (Optional).
• Updated documentation to align with changes (Optional).
• Verified no breaking changes, or prepared solutions for any occurring breaking changes (Optional).
• My change does not involve the above items.

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