fix(agent): keep ChatSessionProvider mounted across /home/* navigations

[Aarjav Jain (A2rjav)]

Summary

Closes #927

ChatSessionProvider was conditionally mounted — only rendered when shouldUseChatSession() returned true (i.e. only on /home/chat). Any navigation away from that route unmounted the provider and destroyed the in-memory useChat message state. Returning to chat started a fresh session with no history.

• ChatSessionProvider now unconditionally wraps all /home/* routes
• Removes the dead shouldUseChatSession helper function
• Removes the useChatSessionOnHome prop from NewTabLayout
• Removes associated tests for the removed function

Test plan

• Open the newtab chat at /home/chat, send a message
• Navigate to another sub-route (e.g. /home/skills, /home/memory)
• Navigate back to /home/chat — previous messages should still be visible
• Verify fresh session still starts on first load (no prior messages on new tab open)
• Confirm no TypeScript errors (bun run typecheck)

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[Aarjav Jain (A2rjav)]

I have read the CLA Document and I hereby sign the CLA

[Nikhil (shadowfax92)]

Thanks so much for contributing to BrowserOS! 🙏

We're doing some housekeeping on our PR queue and closing out PRs that have been open for more than 7 days. This isn't a reflection on your work — we really appreciate the time and effort you put in.

If this is still relevant, please feel free to reopen it or open a fresh PR and we'll take another look. Thanks again for being part of the project! 🚀