feat: show owner info in admin pages

- Add Owner column to AdminRuns.tsx and AdminGenlockes.tsx
- Add owner filter dropdown to both admin pages
- Add owner field to GenlockeListItem schema (resolved from first leg's run)
- Update frontend types for GenlockeListItem

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

.beans/nuzlocke-tracker-2fp1--show-owner-info-in-admin-pages.md

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+---
+# nuzlocke-tracker-2fp1
+title: Show owner info in admin pages
+status: in-progress
+type: feature
+priority: normal
+created_at: 2026-03-21T12:18:51Z
+updated_at: 2026-03-21T12:37:36Z
+parent: nuzlocke-tracker-wwnu
+---
+
+## Problem
+
+Admin pages (`AdminRuns.tsx`, `AdminGenlockes.tsx`) don't show which user owns each run or genlocke. This makes it hard for admins to manage content.
+
+## Approach
+
+### Backend
+- The `/api/runs` list endpoint already returns run data — verify it includes `owner` (id + email). If not, add it to the response schema.
+- For genlockes, ownership is inferred from the first leg's run owner. Add an `owner` field to the genlocke list response that resolves from the first leg's run.
+
+### Frontend
+- `AdminRuns.tsx`: Add an "Owner" column showing the owner's email (or "No owner" for legacy runs)
+- `AdminGenlockes.tsx`: Add an "Owner" column showing the inferred owner from the first leg's run
+- Add owner filter dropdown to both pages
+
+## Files to modify
+
+- `backend/src/app/api/runs.py` — verify owner is included in list response
+- `backend/src/app/api/genlockes.py` — add owner resolution to list endpoint
+- `backend/src/app/schemas/genlocke.py` — add owner field to `GenlockeListItem`
+- `frontend/src/pages/admin/AdminRuns.tsx` — add Owner column + filter
+- `frontend/src/pages/admin/AdminGenlockes.tsx` — add Owner column + filter
+- `frontend/src/types/game.ts` — update types if needed
+
+## Checklist
+
+- [x] Verify runs list API includes owner info; add if missing
+- [x] Add owner resolution to genlocke list endpoint (from first leg's run)
+- [x] Update `GenlockeListItem` schema to include owner
+- [x] Add Owner column to `AdminRuns.tsx`
+- [x] Add Owner column to `AdminGenlockes.tsx`
+- [x] Add owner filter to both admin pages