phinx: Can't update database in migration

I’m trying to run a loop over a particular large database table which can’t be loaded into memory at the same time. I can’t really see much wrong with what I wrote. But perhaps there is something I’m missing.

The up() method looks like this

$processed = 0;
$tables = "countries"

while(true){
	/** @var PDOStatement $stmt */
	$stmt = $this->query("select id,name from $table order by id limit 100 offset $processed");

	if($stmt->rowCount() === 0){
		print("No more data in table '$table'\n");
		break;
	}

	while($row = $stmt->fetch()){
		$id = $row["id"];
		$this->execute("update $table set slug='hello' where id='$id'");
		$processed++;
	}
}

At the end, I expected that the table would hold slugs with hello in them. But to my surprise, it’s a completely empty column.

What am I doing wrong here? I must be blind to something.