feat: Add Matrix infrastructure (Synapse + Element Web)

- Synapse homeserver.yaml configuration
- Element Web config.json
- PostgreSQL init script for synapse DB
- Nginx gateway configuration
- Docker Compose for Matrix stack
- README_MATRIX.md documentation

infra/matrix/postgres/init.sql

@@ -0,0 +1,27 @@
+-- Matrix Synapse PostgreSQL initialization
+-- Run this on the existing dagi-postgres instance
+
+-- Create synapse database
+CREATE DATABASE synapse
+  ENCODING 'UTF8'
+  LC_COLLATE='C'
+  LC_CTYPE='C'
+  template=template0;
+
+-- Create synapse user (password should be set via env variable)
+CREATE USER synapse WITH ENCRYPTED PASSWORD 'CHANGE_ME_IN_PRODUCTION';
+
+-- Grant privileges
+GRANT ALL PRIVILEGES ON DATABASE synapse TO synapse;
+
+-- Connect to synapse database and set up extensions
+\c synapse
+
+-- Required extensions for Synapse
+CREATE EXTENSION IF NOT EXISTS pg_trgm;
+
+-- Grant schema permissions
+GRANT ALL ON SCHEMA public TO synapse;
+ALTER DEFAULT PRIVILEGES IN SCHEMA public GRANT ALL ON TABLES TO synapse;
+ALTER DEFAULT PRIVILEGES IN SCHEMA public GRANT ALL ON SEQUENCES TO synapse;
+