Well, there is this:Has there been any information/speculation about the sizes of the ships in this show?

I don't think so. It seems clear to me that Discovery has a much longer and thinner silhouette than the original Enterprise. On the other hand, the shuttle bay has about the same height as the Constitution class, and the bridge module is about the same size. This tells me the proportions of most of its main features are comparable, which means we have a good estimate for length and width.Its about the same length as the 1701 more or less
As in the above diagram, which seems to draw on the same cues, discovery is considerably longer than 1701, easily in the 700 meter range (so the 790 figure from Trekyards could well be correct), which would give Discovery about 18 decks and a somewhat greater volume than the Constitution as well.
In this case, size is almost meaningless to compare; Shenzhou is a bulky vessel that consists almost entirely of saucer and a smallish engineering section attached to its belly. The saucer section alone is probably the size size as the Constitution's saucer if not slightly larger, with the long nacelles extending aft behind it. That would give it an overall length of about 300 meters or more; longer than the TOS Constitution, but still smaller in every way that counts.The Shenzou looked around half the size of the 1701, based on the picture we were shown of Burnham standing on the edge of the saucer, both the engineering section and the saucer itself look considerably smaller than the 1701.
It's at least 600 meters measuring from the shuttlebay to the front of the saucer. Those ample nacelles add a bit to the profile, though.I would be fine with a big 500-600m Discovery but it really doesn't look anything like that big to the naked eye in the footage we have seen so far