ThemeGuessGame's constructor permanently binds click/mousemove/document
listeners onto the single shared #code-canvas/#category-panel. Solo,
matchmaking, and private-room flows each independently constructed their
own instance, so using more than one mode in the same page load (e.g.
Solo then Find Match) left multiple instances double-bound to the same
DOM, corrupting whichever mode was used first.
Add game/sharedGame.ts: a single lazily-constructed instance, reused via
setTheme/setSnippet and now-mutable onCategoryAssigned across every
flow. main.ts, matchmakingFlow.ts, and privateRoomFlow.ts now call
getSharedGame() instead of `new ThemeGuessGame(...)`.
Verified via CDP DOMDebugger.getEventListeners against a live session:
exactly one click/mousemove listener on #code-canvas after playing a
Solo round followed by a real matched Matchmaking round in the same
page load (previously would have been two of each).