M6.5: enroll matrix-synapse (recipe #4, DB+media/large-volume) — install verified green

install 2 passed on host (~2.7m): synapse client API 200 + real versions JSON, no extra config
(SYNAPSE_SERVER_NAME=DOMAIN). upgrade/backup author postgres-marker assertions exercising the
recipe's pg_backup.sh dump/restore hook (the meaningful matrix data path); verifying next.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

tests/matrix-synapse/test_install.py

@@ -0,0 +1,21 @@
+"""matrix-synapse — install stage (recipe #4, DB + media store). D2 install: the synapse client API
+answers 200 over real HTTPS through the gateway (nginx -> synapse). The base recipe has no browser
+UI (element-web is an addon), so the functional assertion is the JSON client API, not Playwright."""
+import json
+import os
+import sys
+
+sys.path.insert(0, os.path.join(os.path.dirname(__file__), "..", "..", "runner"))
+from harness import lifecycle  # noqa: E402
+
+
+def test_client_api_healthy(deployed_app):
+    status = lifecycle.http_get(deployed_app, "/_matrix/client/versions")
+    assert status == 200, f"expected 200 from {deployed_app}/_matrix/client/versions, got {status}"
+
+
+def test_client_api_advertises_versions(deployed_app):
+    """The client-API version document is real synapse JSON (proves the app, not just a proxy 200)."""
+    body = lifecycle.http_body(deployed_app, "/_matrix/client/versions")
+    doc = json.loads(body)
+    assert isinstance(doc.get("versions"), list) and doc["versions"], "no matrix client versions advertised"