Well, I would start by noting that not everyone in the 19th century was using equal amounts of coal. Not only was there the option of wood, but burning coal fires wasn't necessarily cheap. As Ruth Goodman's "How to be a Victorian" (2013) says in certain rural areas it was more affordable to burn wood from local trees when coal mines were too far away. And Goodman also notes that even wealthy upper-middle families didn't have their coal fires lit all the time. Even with the abundant amount of coal being mined at this time, given how much of it was set aside for cooking, vehicles and industrial use it wasn't something to waste. A coal fire just for heat and lightning was a luxury when warm clothing and candles were everyday cheaper alternatives (plus there was the increasing use of the modern lightning solutions of gas and electric).

One point of how they dealt with soot and coal dust is that fire-screens were common, and as noted in "The Victorian Parlour: A Cultural Study" (Thad Logan, 2001) coal fires don't actually produce many sparks so fire screens could be made of wood, fabric or even paper mache'. Among those who could afford to produce it or buy it, fire screen could even display elaborate needlework in the main body of the screen (with a studier wood or metal frame). Alison Ravetz ("The Victorian Coal Kitchen and Its Reformers", 1968) also noted that the new kitchen ranges had "soot-doors" which provided access to sweeping while limiting the amount of waste that came out, although this still required the build-up to be cleaned up regularly in the same way he would the ash around a wood fire. Colin Fanning ("‘The Indispensable Agent’: Coal and Its Displacements in Victorian Britain", 2020) also notes that devises that produces less smokes, soot or other fire-related uncleanliness were favoured as a major criterion, and a range of equipment including tongs, coal boxes and cinder pails were used to clean up soot, ashes and dust. One other thing that Logan brings up as another way it was dealt with; the servants did it.

It is noted in "The Chimney of the World: A History of Smoke Pollution in Victorian and Edwardian Manchester" (Stephen Mosley, 2001), that dealing with smoke and soot in cleaning was "an arduous daily battle". And for middle-class people and above, domestic help would have done the bulk of the work. This dirtying wasn't just from coal and wood use in the home, it was also from anything in the area which might have been blown in or trafficked on shoes. Given the increasing pollution Mosley describes, it was definitely a real issue. As Logan notes, a contemporary 1880's estimate of a full clean for a drawing room was three hours, including both dusting and the laundering of things like carpets and curtains to be washed. The wives would generally also contribute at a managerial level if nothing else, especially in poor or working class families were they would be doing more the brunt of that labour. However, Stephen Mosley own comparison of this situation to the modern day reminds that this wasn't necessarily a unique or especially bad problem. It would be a mistake to fall for the stereotype that Victorian cities and towns were uniquely dirty in anyway, a stereotype that has been employed with pretty much every time period before the 20th century I would note. Mosley also notes that were campaigns about smoke pollution so it was not an unrecognised problems, there were attempts to reduce smoke output, although campaigns did not always gain traction.

On the question of why black, I would note that there was a general cultural progression from the late 18th century onwards to the arguable apex around the 1880s towards sombre, dark clothing, especially for men. This was very much to do with the gentry modernist desire to portray themselves as serious business-people in contrast to a supposedly idle aristocrat, which was in turn increasingly adopted by the majority of society as it became fashionable. We could call this a kind of false humility. There was a desire to look professional and not overly fancy and bright, but there was no lack of expense and attention to detail in the construction, design and tailoring of men's outfits in the mid-to-late 19th century. Especially as aristocrats and monarchs adopted this fashion, it was very much a performative and limited notion of humility. The gendered division of this is particularly revealing of the cultural motives for it, women were allowed to be more colourful and silky because they were supposed to be desirable and delicate, whereas sombre clothing heavier in wool was a kind of masculine display. This makes no sense if one's aim is primarily to reduce the need for cleaning.

The use of black, brown and grey as the main colours in men's clothing was certainly not primarily because of coal soot in particular. It is noteworthy that these colours were valued for showing dirt less easily than white, one of the most prestigious colours for outerwear given this and the amount of bleaching it took to get a shiny white. But black wasn't the most practical colour though, that would probably be brown, given black was reasonably expensive traditionally and usually had multiple layers of blue and/or red underneath to prevent it from turning brown as it aged. The working class and poor would have had more brown and less black than the middle and upper class. The popularisation in the UK of mourning wear after the death of Prince Albert was also probably a factor in trending black. And let us not forget pure aesthetic taste. The effect of good quality black men's wear in flattering his appearance was often commented upon,

In conclusion, there were definitely solutions employed to minimise, clean-up and sometimes even disguise soot, dust and smoke. But it wasn't always terrible, depending on how much coal burning was happening in your vicinity it might be a much smaller issue in some rural areas, or a big one in industrial areas. And similarly, it is unlikely that the fashion for black and other practical colours was primarily because of soot, given the fashion trend started earlier and went up-and-down with different periods (the colour brightening in the 1890's and 1900s despite continuing industrialisation). There were other factors including gentry culture, gender roles, mourning wear and pure aesthetic taste.