RE: Could not insert term into the database. Similarly it wont let me add any entries either.
The only reason errors like this would occur would be if the tables in the WordPress database have been removed or out of date.
Is this a new installation of Connections or an old one? Have you moved the site?
RE: message regarding PHP version also comes up we are using PHP 7.3
This is simply a information only message. Connections does work fine on newer versions. Connections used to have a minimum requirement of PHP 5.2. So, the max version had to be 7.1. The reason is new versions of PHP deprecates several functions that Connections uses. This mean at some point in 10 years PHP will remove those functions. I have bumped the minimum version to 5.4. Which means I can bump the max version to 7.3 (and newer) after those deprecated functions are remove from Connections. This important bit is that those function will continue to function normally until removed.
So, the short answer is, the PHP version is not the source of the issue you are experiencing.