feat(settings): keep the game tab when switching games

Codes in one game now opens Codes in the next. The reader app holds the
tab and GameSettings reads it, instead of each game page minting its own.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/DESIGN.md

@@ -637,7 +637,8 @@ legend on the same baseline as "Next: …".
 - **Settings.** About, Changelog, Data & sources (list options first), Region & time, Appearance
   (interface, theme, scheme, urgency colours, default view, game order, timeline design, focus bar,
   checklist group), Your own events and games, Backup (tiers plus a manual "Your backups" list), and
-  per-game Setup / Codes / About.
+  per-game Setup / Codes / About. Switching to another game keeps the open tab (2026-10-20, owner):
+  Codes in one game opens Codes in the next.
 - **Redeem codes (2026-10-18, owner).** A game's Codes tab lists the codes still to use first. A
   code redeemed on every server the reader plays, or past its stated expiry, is greyed and struck
   through in a "Redeemed or expired" section below, with its Redeemed box still there to undo. A