Add and run script for upgrading PostgreSQL of matrix host

The script is a modified version of the script shown in the PostgreSQL
Upgrading section of the NixOS manual. Our version is for upgrading
PostgreSQL 14 to 15.
Basically do steps 1-3 of the section.

Link to the section:
https://nixos.org/manual/nixos/stable/#module-services-postgres-upgrading

config/hosts/matrix/postgresql.nix

@@ -14,4 +14,33 @@
 
     dataDir = "/mnt/data/postgresql/${config.services.postgresql.package.psqlSchema}";
   };
+
+  # Modified version of the script for upgrading PostgreSQL from here:
+  # https://nixos.org/manual/nixos/stable/#module-services-postgres-upgrading
+  environment.systemPackages = [
+    (let
+      newPostgres = pkgs.postgresql_15;
+    in pkgs.writeScriptBin "upgrade-pg-cluster" ''
+      set -eux
+
+      systemctl stop matrix-synapse.service
+      systemctl stop postgresql.service
+
+      export NEWDATA="/mnt/data/postgresql/${newPostgres.psqlSchema}"
+
+      export NEWBIN="${newPostgres}/bin"
+
+      export OLDDATA="${config.services.postgresql.dataDir}"
+      export OLDBIN="${config.services.postgresql.package}/bin"
+
+      install -d -m 0700 -o postgres -g postgres "$NEWDATA"
+      cd "$NEWDATA"
+      sudo -u postgres $NEWBIN/initdb -D "$NEWDATA"
+
+      sudo -u postgres $NEWBIN/pg_upgrade \
+        --old-datadir "$OLDDATA" --new-datadir "$NEWDATA" \
+        --old-bindir $OLDBIN --new-bindir $NEWBIN \
+        "$@"
+    '')
+  ];
 }