Add Matrix homeserver with MatrixRTC calling support

- Synapse + PostgreSQL + coturn + LiveKit + lk-jwt-service
- Caddy entries for mtx.alogins.net, lk.alogins.net, lkjwt.alogins.net
- well-known endpoints for Matrix client/server discovery and RTC transport
- Users: admin, elizaveta, aleksandra

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

matrix/docker-compose.yml

@@ -0,0 +1,73 @@
+services:
+  synapse:
+    image: matrixdotorg/synapse:latest
+    container_name: synapse
+    restart: unless-stopped
+    volumes:
+      - ${SYNAPSE_DATA}:/data
+      - /etc/localtime:/etc/localtime:ro
+    environment:
+      - SYNAPSE_CONFIG_PATH=/data/homeserver.yaml
+    ports:
+      - "127.0.0.1:8008:8008"
+    depends_on:
+      - db
+    networks:
+      - matrix
+      - frontend
+
+  db:
+    image: postgres:16-alpine
+    container_name: synapse-db
+    restart: unless-stopped
+    environment:
+      - POSTGRES_USER=${POSTGRES_USER}
+      - POSTGRES_PASSWORD=${POSTGRES_PASSWORD}
+      - POSTGRES_DB=${POSTGRES_DB}
+      - POSTGRES_INITDB_ARGS=--encoding=UTF-8 --lc-collate=C --lc-ctype=C
+    volumes:
+      - ${POSTGRES_DATA}:/var/lib/postgresql/data
+      - /etc/localtime:/etc/localtime:ro
+    networks:
+      - matrix
+
+  lk-jwt-service:
+    image: ghcr.io/element-hq/lk-jwt-service:latest
+    container_name: lk-jwt-service
+    restart: unless-stopped
+    ports:
+      - "127.0.0.1:8009:8080"
+    environment:
+      - LIVEKIT_JWT_BIND=:8080
+      - LIVEKIT_URL=wss://lk.alogins.net
+      - LIVEKIT_KEY=${LIVEKIT_KEY}
+      - LIVEKIT_SECRET=${LIVEKIT_SECRET}
+      - LIVEKIT_FULL_ACCESS_HOMESERVERS=mtx.alogins.net
+    extra_hosts:
+      - "mtx.alogins.net:host-gateway"
+      - "lk.alogins.net:host-gateway"
+
+  livekit:
+    image: livekit/livekit-server:latest
+    container_name: livekit
+    restart: unless-stopped
+    network_mode: host
+    volumes:
+      - ./livekit/livekit.yaml:/etc/livekit.yaml:ro
+    command: --config /etc/livekit.yaml
+
+  coturn:
+    image: coturn/coturn:latest
+    container_name: coturn
+    restart: unless-stopped
+    network_mode: host
+    volumes:
+      - ./coturn/turnserver.conf:/etc/coturn/turnserver.conf:ro
+      - /etc/localtime:/etc/localtime:ro
+
+networks:
+  matrix:
+    driver: bridge
+    internal: true
+  frontend:
+    driver: bridge