As of last October (So pre-Switch release), sales were "over 4 million" so had likely just hit 4 million when SE reported them. As well we know that Dragon Quest XI S has sold 450k in Japan. That would leave with that information alone, 5.5-4.45 sales as Western sales of XI S. Of course, this doesn't account for digital sales for XI S in Japan which still haven't been accurately reported, and it is probable that some sales occurred for the Western release past 2018, so its likely not quite a million, however this means that shipments plus digital sales for XI S are likely approaching a million in the West which is pretty good, especially given they were only around 600k in the West when data was released last year (early November). https://square-enix-games.com/en_GB/news/dragon-quest-xi-echoes-of-an-elusive-age-ships-over-4-million-copies-globally
Edit: Also as I should have pointed out "West" really means not Japan since Asian sales are lumped in there as well but its hard to know how much that affects the numbers.