<!-- CURSOR_SUMMARY -->
> [!NOTE]
> Adds analytics context to chat submissions.
> 
> - Update `ChatInput.tsx` to capture `chat:submit` with `{ chatMode:
settings?.selectedChatMode }`
> - Update `HomeChatInput.tsx` to capture `chat:home_submit` with `{
chatMode: settings?.selectedChatMode }`
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
2b84eb984bd1c5368c1aeba03db5fd1a2f431bd9. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

<!-- This is an auto-generated description by cubic. -->
## Summary by cubic
Add chatMode to PostHog analytics on chat submission to track which chat
mode was used. Applies to chat:submit and chat:home_submit events.

<sup>Written for commit 2b84eb984bd1c5368c1aeba03db5fd1a2f431bd9.
Summary will update on new commits.</sup>

<!-- End of auto-generated description by cubic. -->