tests/synapse-{postgres,sqlite}: init

This commit ports some of the integrations tests from nixpkgs to be used for
the matrix-synapse-next module.

tests/synapse-sqlite/default.nix

@@ -0,0 +1,29 @@
+# Modified from https://github.com/NixOS/nixpkgs/blob/nixos-26.05/nixos/tests/matrix/synapse.nix
+
+{ pkgs, ... }:
+{
+  name = "matrix-synapse-sqlite";
+  nodes = {
+    server = args: {
+      imports = [
+        ../../synapse-module
+      ];
+
+      services.matrix-synapse-next = {
+        enable = true;
+        settings = {
+          database.name = "sqlite3";
+          server_name = "example.com";
+        };
+      };
+    };
+  };
+
+  testScript = ''
+    server.wait_for_unit("matrix-synapse.service")
+    server.wait_until_succeeds(
+        "curl --fail -L --unix-socket /run/matrix-synapse/matrix-synapse.sock http://localhost/"
+    )
+    server.succeed("[ -e /var/lib/matrix-synapse/homeserver.db ]")
+  '';
+}