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/api/src/routes/auth.ts

@@ -68,7 +68,7 @@ authRouter.get("/callback", async (context) => {
       await prisma.gameState.create({
         data: {
           discordId: player.discordId,
-          state: initialState,
+          state: initialState as unknown as never,
           updatedAt: now,
         },
       });