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/profile.ts

@@ -5,10 +5,11 @@ import type {
 } from "@elysium/types";
 import { DEFAULT_PROFILE_SETTINGS } from "@elysium/types";
 import { Hono } from "hono";
+import type { HonoEnv } from "../types/hono.js";
 import { prisma } from "../db/client.js";
 import { authMiddleware } from "../middleware/auth.js";
 
-export const profileRouter = new Hono();
+export const profileRouter = new Hono<HonoEnv>();
 
 const VALID_NUMBER_FORMATS = new Set(["suffix", "scientific", "engineering"]);