## Summary
- Set `isPro` as a person property in PostHog when settings are loaded
and updated
- Enables segmenting analytics by pro user status
- Reuses existing `hasDyadProKey` helper for consistency

## Test plan
- [x] Lint passes
- [x] TypeScript type check passes
- [ ] Manual verification that PostHog receives the person property

#skip-bugbot

🤖 Generated with [Claude Code](https://claude.com/claude-code)

<!-- This is an auto-generated description by cubic. -->
---
## Summary by cubic
Set an isPro person property in PostHog when settings load and whenever
they update, enabling analytics segmentation by Pro status. Reuses
hasDyadProKey and aligns the app:initial-load event’s isPro with the
same logic.

<sup>Written for commit 376d4ab5ca9102c25edd43b83e1ea4d8622aa171.
Summary will update on new commits.</sup>

<!-- End of auto-generated description by cubic. -->
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>