Modern PostgreSQL supports the RETURNING keyword. Basically, you treat the statement as a one line SELECT afterwards.

my $sth = $dbh->prepare_cached("INSERT INTO bla (colname1, colname2) V
+ALUES (?, ?) RETURNING bla_id")
    or croak($dbh->errstr);
$sth->execute($val1, $val2) or croak($dbh->errstr);
my $line = $sth->fetchrow_hashref;
$sth->finish;
$dbh->commit;

print "Inserted data with new primary key ", $line->{bla_id}, "\n";
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See also: https://www.postgresql.org/docs/current/dml-returning.html