The solution turned out to be quite straightforward, and I'm a bit embarrassed that I didn't realize it earlier. I needed to access the protected connection property of the parent class and execute a query to conditionally handle my migration. (Thanks to @iainn for the suggestion.)

For the specific case where id = 0, @AymDev was correct in pointing out that it was a SQL mode issue. The solution involved setting the SQL mode to include NO_AUTO_VALUE_ON_ZERO before the insertion and then resetting it afterward.

public function up(Schema $schema): void
{

    $r = $this->connection->prepare('SELECT COUNT(*) FROM meal_moment WHERE id = 0')
        ->executeQuery()
        ->fetchOne();

    if ($r == 0) {
        $modes = $this->connection->prepare("SELECT @@sql_mode;")
            ->executeQuery()
            ->fetchOne();

        $this->addSql("
            SET sql_mode = CONCAT(@@sql_mode, ',NO_AUTO_VALUE_ON_ZERO');
            INSERT INTO `meal_moment` (`id`, `name`, `code`, `ordre`, `customer_id`) VALUES (0, 'Aucun', 'Aucun', 0, 0);
            SET sql_mode = :modes
            ", ['modes' => $modes]);

    }
    $this->addSql("UPDATE `order` SET mealmoment_id = 0 WHERE mealmoment_id IS NULL");

}

public function down(Schema $schema): void
{
    $this->addSql('UPDATE `order` SET mealmoment_id = NULL WHERE mealmoment_id = 0');
    $this->addSql('DELETE FROM meal_moment WHERE id = 0');

}