I got the USA The Shining 4K set from Best Buy today, and I checked the disc and the remastered Blu-ray that comes with the 4K does NOT include the trailer (and, for the record, it's not on the 4K disc either).
While I can't confirm that the Blu-ray that comes with the 4K in other regions does not include the trailer, I would imagine it is the same across regions.
Also, I can confirm that all extras are 480i on both the original USA Blu-ray (which I also currently own) and the remastered USA Blu-ray that comes with the 4K.