feat(live-streaming): implement live streaming and spectator mode

[mubashqoz-eng]

Closes #441

Overview

Adds a self-contained backend module for live streaming and spectator mode:
stream lifecycle, spectator joining, real-time chat, viewer tracking, adaptive
quality, recording, moderator tools and viewership analytics. It follows the
src/community-events module shape (entities + DTOs + service + controller +
module) and adds a Socket.IO gateway on the /streams namespace.

The issue asks for ten tasks; this implements all of the acceptance criteria
through a single new src/live-streaming module and wires it into AppModule.

Related Issue

Closes #441

Changes

• [ADD] src/live-streaming/entities/ — LiveStream (status machine, cached
  and peak viewer counts, recording state), StreamViewer (soft membership so
  viewership is analysable), StreamChatMessage (soft deletes keep the audit
  trail), StreamModerationAction (immutable decisions; enforcement reads them).
• [ADD] src/live-streaming/dto/ — validated create/join/chat/moderation
  DTOs with Swagger metadata.
• [ADD] src/live-streaming/live-streaming.service.ts — the behaviour:
  create/start/end/cancel, join/leave/count, deterministic
  qualityForBandwidth, chat post/history, moderator tools, recording, and a
  getAnalytics aggregate. Host and moderator permissions are enforced in the
  service; a finished stream cannot be started or joined, a banned viewer cannot
  join or chat, and an unexpired timeout blocks both.
• [ADD] src/live-streaming/live-streaming.controller.ts — REST surface for
  every operation. The caller's id travels in x-user-id; binding that header to
  the JWT guard is a gateway-shell decision, and the service is where the real
  host/moderator check lives.
• [ADD] src/live-streaming/gateways/live-streaming.gateway.ts — stream:join,
  stream:leave, stream:chat, stream:quality. Chat broadcasts to the
  stream:<id> room; counts are re-read from the roster so two sockets cannot
  drift the number; a disconnect leaves on behalf of the socket's stored user.
• [ADD] src/live-streaming/live-streaming.module.ts and
  src/migrations/1760000000000-CreateLiveStreamingTables.ts — module wiring and
  the four-table schema with indexes.
• [MODIFY] src/app.module.ts — import LiveStreamingModule.
• [ADD] src/live-streaming/README.md — model, routes, gateway events,
  quality ladder and migration.

Verification Results

npx jest src/live-streaming
npx tsc --noEmit
npx eslint "src/live-streaming/**/*.ts"

Acceptance check:

Acceptance criterion	Status
Streams created and managed	✅ scheduled/live/ended/cancelled; start/end/cancel host-only, idempotent where safe
Spectators join successfully	✅ join is idempotent; viewer count is read from the active roster and peak is monotonic
Chat real-time	✅ stream:chat broadcasts to the stream room; REST history excludes deleted messages
Quality adapts to bandwidth	✅ pure qualityForBandwidth ladder, unit-tested at every boundary
Recording functional	✅ start/stop by the host; ending a recorded stream finalises a URL
Analytics track viewership	✅ current/peak/total viewers, chat count, moderation count, quality distribution, duration
Moderator tools	✅ ban/unban/timeout/delete/pin/clear with an immutable action log; host or assigned moderator only
Comprehensive tests	✅ 42 tests (service + gateway)

• npx jest src/live-streaming: 2 suites, 42 tests, all passing.
• npx jest test/spectator/spectator.service.spec.ts: passing (unchanged).
• npx tsc --noEmit: 207 pre-existing errors across the repo; none in any file
  this PR touches.
• npx eslint "src/live-streaming/**/*.ts": 3 errors, all the
  no-unsafe-return / no-unsafe-assignment pattern in the generic test-repo
  mock that existing specs (community-events.service.spec.ts) also carry.

Blockers and pre-existing failures (not from this diff)

• main is red before this change. npm run typecheck fails with 207
  errors in files unrelated to this diff (for example
  src/skill-rating/elo.service.spec.ts importing ../elo.service from the
  wrong directory, src/users/users.service.ts importing a missing
  common/pagination, src/replay/tests/replay.integration.spec.ts referencing
  an undefined analyticRepo). Because CI's typecheck step is not
  tolerated (lint:check and format:check are), CI cannot go green for any PR
  until those are fixed separately.
• test/spectator/multiplayer.spectator.spec.ts fails on main with
  Nest can't resolve dependencies of the MultiplayerGateway ... EventEmitter,
  independent of this change.
• npx jest on the whole suite is large and mixed; I verified the suites this
  module can affect and left the unrelated pre-existing failures alone.

Notes for the reviewer

• The module is not auth-guarded; it trusts x-user-id and enforces host and
  moderator authority inside the service. If the repo standard is to attach
  JwtAuthGuard at the controller, that is a one-line change I can fold in.
• getAnalytics derives currentViewers and the quality distribution from the
  active roster (source of truth) while LiveStream.viewerCount is a cached
  read; a reconciliation job is not needed but the two are deliberately both
  asserted in tests.

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