Presently "Copy as SQL INSERT-VALUES statement" (ran on selection in table content tab) produces a non-runnable SQL if application table schema is not listed in search_path.
Most application I know do not put their tables into public schema; it is a widely agreed to be a poor design choice. They create their own, often multiple, schemes. Also most applications to not require patching search_path in the server config to include their schemes in it in order to use the application.
While "Copy as SQL INSERT-VALUES statement" feature is still helpful, it requires manual adjustment and if a developer is not careful (I know this is a bogus argument) may result in rogue inserted rows.
Conceptually it is never wrong to use qualified table names, however for some databases (specifically PostgreSQL) using non-qualified table names almost always produces non-runnable SQL when the table is not in public or pg_catalog schema.
The same applies to some other "Copy as SQL" actions used on the table content tab.
This snapshot should fix the problem for you.