fix: enable agent mode switch on new conversation page without websocket

[nehaprasad-dev]

Summary

• Enable Code/Plan when no conversation is open.
• Match overflow agent menu behavior.
• Link LLM chip to /settings/llm.

Issue Number

fix : #689

How to Test

• Cloud backend → home / new conversation.
• Code/Plan is clickable.
• LLM chip → /settings/llm.

Video/Screenshots

• N/A

Type

• Bug fix

Notes

• Cloud LLM still changes via settings, not in-chat profiles.

[vercel]

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[DevinVinson]

Hi @nehaprasad-dev - Thank you for this PR! I asked about the fix that was merged in by @hieptl to fix #689 and he mentioned we would not be able to support the Plan mode just yet: https://openhands-ai.slack.com/archives/C06QT0AGY4W/p1779981817014669

If you want to join the proj-canvas channel in slack that would help to co-ordinate and give feedback too!