fix: resolve pre-existing TypeScript strictness build errors

- Add @types/node to API devDependencies
- Create HonoEnv type and apply to all routers + auth middleware for
  proper context.get/set("discordId") typing
- Use conditional spreads for exactOptionalPropertyTypes dailyChallenges
  in GameContext, tick engine, and prestige route
- Use conditional spread for optional signature in SaveRequest calls
- Add non-null assertions in shuffle/template index for noUncheckedIndexedAccess
- Cast GameState to never for Prisma InputJsonValue fields
- Exclude vite.config.ts from web tsconfig (it runs in Node context)

apps/web/tsconfig.json

@@ -7,5 +7,5 @@
     "lib": ["ES2022", "DOM", "DOM.Iterable"],
     "target": "ES2022"
   },
-  "exclude": ["test/**/*.ts", "test/**/*.tsx"]
+  "exclude": ["test/**/*.ts", "test/**/*.tsx", "vite.config.ts"]
 }