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/web/src/context/gameContext.tsx

@@ -243,6 +243,11 @@ interface GameContextValue {
   isLoading: boolean;
   error:     string | null;
 
+  /**
+   * Whether the player is currently a member of the NHCarrigan Discord server.
+   */
+  inGuild: boolean;
+
   /**
    * Click the crystal to earn gold.
    */
@@ -694,6 +699,7 @@ export const GameProvider = ({
   const [ schemaOutdated, setSchemaOutdated ] = useState(false);
   const [ saveSchemaVersion, setSaveSchemaVersion ] = useState(0);
   const [ currentSchemaVersion, setCurrentSchemaVersion ] = useState(0);
+  const [ inGuild, setInGuild ] = useState(false);
   const [ unlockedCodexEntryIds, setUnlockedCodexEntryIds ] = useState<
     Array<string>
   >([]);
@@ -731,6 +737,7 @@ export const GameProvider = ({
       setSchemaOutdated(data.schemaOutdated);
       setSaveSchemaVersion(data.state.schemaVersion ?? 0);
       setCurrentSchemaVersion(data.currentSchemaVersion);
+      setInGuild(data.inGuild);
 
       // Fetch number format preference from profile (fire-and-forget, non-blocking)
       void fetch(`/api/profile/${data.state.player.discordId}`).
@@ -2303,6 +2310,7 @@ export const GameProvider = ({
       forceUnlocks,
       formatNumber,
       handleClick,
+      inGuild,
       isLoading,
       isSyncing,
       lastSavedAt,
@@ -2374,6 +2382,7 @@ export const GameProvider = ({
     error,
     flushBossLoreToasts,
     forceSync,
+    inGuild,
     forceUnlocks,
     handleClick,
     isLoading,