diff --git a/superset/db_engine_specs/postgres.py b/superset/db_engine_specs/postgres.py
index 1945fa3f303..406e85effe2 100644
--- a/superset/db_engine_specs/postgres.py
+++ b/superset/db_engine_specs/postgres.py
@@ -821,6 +821,32 @@ WHERE datistemplate = false;
                 )
             }
 
+    @classmethod
+    def get_schema_names(cls, inspector: Inspector) -> set[str]:
+        """
+        Return all schema names, excluding the ``pg_``-prefixed Postgres
+        system schemas (e.g. ``pg_catalog``, ``pg_toast``).
+
+        SQLAlchemy's Postgres dialect filters out system schemas with the
+        query ``nspname NOT LIKE 'pg_%'``. Since ``_`` is a single-character
+        wildcard in SQL ``LIKE`` patterns, this unintentionally excludes any
+        user-defined schema that merely starts with ``pg`` followed by any
+        other character (e.g. ``pgsql``, ``pgstats``), not only the
+        ``pg_``-prefixed system schemas. Matching on the literal ``pg_``
+        prefix instead keeps those user-defined schemas.
+
+        TODO: drop this override once sqlalchemy/sqlalchemy#13471 is merged
+        and released, and SQLAlchemy is bumped past that version.
+        """
+        with inspector.engine.connect() as conn:
+            return {
+                name
+                for (name,) in conn.execute(
+                    text("SELECT nspname FROM pg_namespace ORDER BY nspname")
+                )
+                if not name.startswith("pg_")
+            }
+
     @classmethod
     def get_table_names(
         cls, database: Database, inspector: PGInspector, schema: str | None
diff --git a/tests/unit_tests/db_engine_specs/test_postgres.py b/tests/unit_tests/db_engine_specs/test_postgres.py
index 287fcec38a3..c1840d9fd71 100644
--- a/tests/unit_tests/db_engine_specs/test_postgres.py
+++ b/tests/unit_tests/db_engine_specs/test_postgres.py
@@ -450,3 +450,33 @@ def test_interval_type_mutator() -> None:
     assert mutator(True) is None
     assert mutator([1, 2, 3]) is None
     assert mutator({"days": 1}) is None
+
+
+def test_get_schema_names_excludes_only_actual_system_schemas(
+    mocker: MockerFixture,
+) -> None:
+    """
+    DB Eng Specs (postgres): Test ``get_schema_names``
+
+    User-defined schemas that merely start with ``pg`` (but are not
+    actual Postgres system schemas, which always start with the literal
+    ``pg_``) must not be filtered out. See issue #30678.
+    """
+    inspector = mocker.MagicMock()
+    inspector.engine.connect().__enter__().execute.return_value = [
+        ("public",),
+        ("pgsql",),
+        ("pgstats",),
+        ("pg_catalog",),
+        ("pg_toast",),
+        ("information_schema",),
+    ]
+
+    schemas = spec.get_schema_names(inspector)
+
+    assert schemas == {
+        "public",
+        "pgsql",
+        "pgstats",
+        "information_schema",
+    }