As @Steve correctly states, Appsheet requires internet presence. Now, I looked at previous posts in this community and found the following method to enable access to your on-premise database:
Some time ago I actually tried the same method mentioned in the referenced post to connect AppSheet to a PostgreSQL database hosted on our company server. The connection worked correctly for a while, but later I was informed by AppSheet that the account I was using did not have the required license type to maintain a direct connection to a database, and that if I did not remove that connection the applications would stop working.
So my specific question is: can this method of connecting to an on-premise PostgreSQL database be used with an AppSheet Core account, or does it require a higher-level license (Enterprise or another plan)?
Yes, connecting an on-premise PostgreSQL database to an AppSheet Core account is possible, but it typically requires configuring the database to accept incoming traffic from AppSheet’s server IP addresses via firewall updates. While direct SQL connector access is often listed under Enterprise plans, Core users can connect on-premise sources if the database is accessible via a public IP and configured for SQL connection.
My suggestion though is to contact support for a more technically knowledgeable person to help you on how to make this configuration