For the dreadnought to be 22 km long and only weight 280,000 tonnes, they'd need to lightweight by over 2000 times relative to the materials technology in the Vesuvius.
For comparison, a rectangular block of Earth sea-level air measuring 22x2x2 km (approximately the presumed size of a box that would enclose the Hvar'kann) would have a mass of approximately 105 million tons. Let's assume for the sake of argument that the Hvar'kann's irregular shape only takes up five percent of this box that is equal to its maximum length, beam, and height. This still makes a 280 thousand ton Hvar'kann a dozen times lighter than the atmosphere that it would contain if it were pressurized to ordinary habitable levels! As such, I'm pretty sure that the dreadnought's mass should be on the order of tens to hundreds of millions of tons if the 22 km length is correct.