chore(o-gui-agent): optimize agent game mode's processing

[ZhaoHeh]

Summary

• Comment out prompts on web uifor game mode
• Fix bug: no pre assisstant message inserted
• Fix bug: repeatly inserting screenshot and assisstant message

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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