feat: grant Elysian role on auth and prompt non-members to join (#134)

## Summary

- Grants the Elysian Discord role to players on login/registration and persists an `inGuild` flag on the Player record
- Connects to the Discord Gateway via WebSocket to keep `inGuild` in sync as players join or leave the server
- Shows a dismissible "Join our community" modal to players who are not yet in the guild
- Hardens `inGuild` exposure through the load endpoint and game context
- Moves all non-secret Discord IDs (guild, role, client, redirect URI) out of env vars and into hardcoded constants; removes them from `prod.env`

## Test plan

- [ ] Lint, build, and test pipeline passes (100% coverage maintained)
- [ ] New player auth grants Elysian role and sets `inGuild: true`
- [ ] Existing player auth re-attempts role grant and updates `inGuild`
- [ ] Join community modal appears for players not in the guild
- [ ] Modal does not reappear within the same browser session after dismissal
- [ ] Gateway correctly sets `inGuild: true/false` on member add/remove events

✨ This issue was created with help from Hikari~ 🌸

Reviewed-on: #134
Co-authored-by: Hikari <hikari@nhcarrigan.com>
Co-committed-by: Hikari <hikari@nhcarrigan.com>

apps/api/src/index.ts

@@ -21,6 +21,7 @@ import { leaderboardRouter } from "./routes/leaderboards.js";
 import { prestigeRouter } from "./routes/prestige.js";
 import { profileRouter } from "./routes/profile.js";
 import { transcendenceRouter } from "./routes/transcendence.js";
+import { connectGateway } from "./services/gateway.js";
 import { logger } from "./services/logger.js";
 
 const app = new Hono();
@@ -68,6 +69,7 @@ const port = Number(process.env.PORT ?? 3001);
 try {
   serve({ fetch: app.fetch, port: port }, () => {
     process.stdout.write(`Elysium API running on port ${String(port)}\n`);
+    connectGateway();
   });
 } catch (error) {
   void logger.error(