You might even want to call it Baroque, and why not? Oh yes, I know that the style is Neo-classical - Bathwick was laid out 1788-1806 after all - but the facades are merely decoration, the icing on a sort of urban form that only appears with the emergence of the Baroque. It could be said to be one of the defining elements of the style. I should add here that Robert Adam's original plan for Bathwick was even more Baroque owing something to Wren's plan for the rebuilding of the City of London, and to the sort of urban forms one associates with Grand Siècle France. Styles do not die; they are not un-invented. Sometimes think of Art and Architectural historians as taxonomists, rather like 19th century naturalists. They might even throw in a few terminal dates too. It's not as though these categories, such as Baroque and Neo-Classical, don't exist only that sometimes the definitions are understood as antithetical to one another, when in fact, there are always elements of continuity. I would argue that this plan represents such a continuity, maybe even a revival.
I didn't realise until researching this post that the Holburne Museum is the focus of a 'patte d'oie' of three radiating streets. Well, you can't get more Baroque than a 'patte d'oie'. Baroque too in the sense of individual units, in this case the house, being subsumed into the greater whole for the sake of urban theatre. And that, it could be argued, is also one of the tendencies of Modernity. But, alas, for all that grandeur and social cachet the scheme, with its long 'palace fronts', was not completed. As with the rest of Bath, development ceased by 1820. Terraces abruptly halt and the next buildings in the street date from the late 19th century. Only on Henrietta St, being that bit closer to the city centre, is there a sense of continuity with a line of early to mid Victorian villas on the west side of the street. Lovely they are too.