feat(amazonq): sync developer profiles to flare chat panel

[jpinkney-aws]

Problem

• developer profiles are only synced to our local agents (/dev, /doc, etc). Now that the main chat panel is served by flare we need to update the profile information when it becomes available so that flare is using the correct profile for the request

Solution

• send profile information to flare on the initial request + subsequent changes to the active profile
• refresh the webview if the profile changes

---

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[github-actions]

• This pull request modifies code in src/* but no tests were added/updated.
  • Confirm whether tests should be added or ensure the PR description explains why tests are not required.
• This pull request implements a feat or fix, so it must include a changelog entry (unless the fix is for an unreleased feature). Review the changelog guidelines.
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[Hweinstock]

Is there a more general place we can put this? I imagine this is useful functionality for all webviews.