hook update_option/updated_option empty $old_value and $value

The syntax should be: add_action('update_option', [$this, 'update'], 10, 3) because your function is accepting 3 arguments:

public function __construct()
{
    add_action('update_option', [$this, 'update'], 10, 3);
}

PS: add_action()‘s reference.

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