feat(#384): Add Synapse + Element Web to docker-compose for dev

- Create docker-compose.matrix.yml as optional dev overlay
- Add Synapse homeserver config with shared PostgreSQL
- Add Element Web client config (port 8501)
- Add bot account setup script (docker/matrix/scripts/setup-bot.sh)
- Add Makefile targets: matrix-up, matrix-down, matrix-logs, matrix-setup-bot
- Document Matrix env vars in .env.example
- Synapse accessible at localhost:8008, Element at localhost:8501
- Usage: docker compose -f docker/docker-compose.yml -f docker/docker-compose.matrix.yml up

Refs #384

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

Makefile

@@ -1,4 +1,4 @@
-.PHONY: help install dev build test docker-up docker-down docker-logs docker-ps docker-build docker-restart docker-test clean
+.PHONY: help install dev build test docker-up docker-down docker-logs docker-ps docker-build docker-restart docker-test clean matrix-up matrix-down matrix-logs matrix-setup-bot
 
 # Default target
 help:
@@ -24,6 +24,12 @@ help:
 	@echo "  make docker-test            Run Docker smoke test"
 	@echo "  make docker-test-traefik    Run Traefik integration tests"
 	@echo ""
+	@echo "Matrix Dev Environment:"
+	@echo "  make matrix-up              Start Matrix services (Synapse + Element)"
+	@echo "  make matrix-down            Stop Matrix services"
+	@echo "  make matrix-logs            View Matrix service logs"
+	@echo "  make matrix-setup-bot       Create bot account and get access token"
+	@echo ""
 	@echo "Database:"
 	@echo "  make db-migrate       Run database migrations"
 	@echo "  make db-seed          Seed development data"
@@ -85,6 +91,19 @@ docker-test:
 docker-test-traefik:
 	./tests/integration/docker/traefik.test.sh all
 
+# Matrix Dev Environment
+matrix-up:
+	docker compose -f docker/docker-compose.yml -f docker/docker-compose.matrix.yml up -d
+
+matrix-down:
+	docker compose -f docker/docker-compose.yml -f docker/docker-compose.matrix.yml down
+
+matrix-logs:
+	docker compose -f docker/docker-compose.yml -f docker/docker-compose.matrix.yml logs -f synapse element-web
+
+matrix-setup-bot:
+	docker/matrix/scripts/setup-bot.sh
+
 # Database operations
 db-migrate:
 	cd apps/api && pnpm prisma:migrate