Since this other thread about ArcGIS Monitor suggests the Datastore and associated database is just a regular PostgreSQL installation, the logical option to monitor your Datastore health would be any of the available (commercial) software packages for monitoring PostgreSQL database health.
E.g. pgAdmin would be a logical choice. DBeaver is another option, and there others out there if you do a bit of searching. Although both of these suggested options are more about database management, and not so much about alerting or warning you when something catastrophic is about to happen. There are other options out there though, that do more of a kind of monitoring job if you do a bit of internet searching.
