I ordered the PA248QV from Asus Store on Wednesday, and received order confirmation emails.
By Friday, having received no dispatch confirmation, I phoned to ask what was up. Was told it was stuck on "processing" for an unknown reason. I would get notification by end of day or early tomorrow (i.e. by Saturday morning), because they needed to check with the warehouse. I got the impression the CS agent was fobbing me off, so was unsurprised by the not having received any email.
The Asus Store is operated by "FiveTech Ltd", which is a trading name for "Laptop Outlet", and if I had thought to check before ordering I would have seen large numbers of bad reviews, and ordered from elsewhere instead.
So now I guess I wait until Monday to see if they actually dispatch it, or I start the hassle of getting a refund and go somewhere reliable.