docs(trellis): update for cloud supabase migration

.trellis/spec/backend/database-guidelines.md

@@ -9,10 +9,25 @@
 This project uses:
 - **SQLAlchemy 2.0** with async support (`asyncpg` driver)
 - **Alembic** for schema migrations
-- **Supabase Auth** as identity source
-- **PostgreSQL** as primary database
+- **Supabase Cloud** for Auth, Database, and Storage
+- **PostgreSQL** as primary database (via Supabase connection pooler)
 - **Soft delete** pattern with `deleted_at` column
 
+### Cloud Supabase Connection
+
+The project uses **Supabase Cloud** with connection pooling:
+
+```bash
+# .env configuration
+ERYAO_DATABASE__HOST=aws-1-us-east-2.pooler.supabase.com
+ERYAO_DATABASE__PORT=5432  # Session pooler (IPv4 compatible)
+ERYAO_DATABASE__NAME=postgres
+ERYAO_DATABASE__USER=postgres.<project-ref>
+ERYAO_DATABASE__PASSWORD=<your-password>
+```
+
+**Note:** Direct database connection (port 5432 on `db.<project-ref>.supabase.co`) requires IPv6 and is not suitable for most development environments. Use the connection pooler instead.
+
 ---
 
 ## Query Patterns
@@ -133,6 +148,8 @@ def downgrade() -> None:
 ./infra/scripts/dev-migrate.sh bootstrap
 ```
 
+**Note:** Cloud Supabase migrations may be slower than local due to network latency. Use appropriate timeouts for migration scripts.
+
 **Alembic is the ONLY source of truth for schema changes.**
 
 ---