Ang Lee (Taiwanese) is probably the most prominent Asian director in Hollywood. He directed Gemini Man (starring Will Smith) amongst many, many other Hollywood movies that showcase a very wide variety of ethnicities (Brokeback Mountain, Crouching Tiger Hidden Dragon, Hulk, etc). The Fast and the Furious franchise also were directed by multiple Asian directors (which is probably why there were an Asian character in the movie at all). If it is a modern take movie (happening in this current time) and based in America, then yes, Asian producers and directors have cast diverse actors to fill roles.
To your other question, it is not simply a question of "ancestral" relevance. It is also a question of historical relevance as to when and how the British empire expanded. In 1813, there were already Asians in England due to silk trade, spice trade, and British colonization of South Asia and trade with China. Although, note that majority of Asians in Britain at the time were not of high status or wealth either.
African folks were more prominent in Italy, Spain, Portugal, and France due to proximity to the Mediterranean and north Africa, hence why there is a Moor genealogical influence to the Portuguese Royal line. Through royals marrying cousins to "keep it in the family," that line now exists through many European royal families, although it is diluted by at least 600 years now...still, it was there. Most European royal lines can trace themselves back to the Castile (Spain). And if we were going to be honest about royal genealogy, the British Royal family is more German than they are British. This includes Charlotte.
On the flip side, England didn't really take a whole lot of interest in colonizing Africa until around 1870 (which opened up immigration), although the British were involved heavily in the African slave trade since around 1640. Majority of these slaves were shipped to British colonies (North America, South America, Caribbeans, etc). In England itself, there were black people there, yes, but until 1807 when the Abolition of Slave Trade Act came to be and in 1834 when slavery was abolished in the British Empire, Africans that found themselves in the British Isles were largely servants with very little possibility for upward mobility.
And if the imagining is how England would have looked like if Queen Charlotte had used her powers to elevate people of color, we're still just seeing "people of color" as black in this representation. Additionally, like I stated in my piece, you would have seen a lot of knighthoods (Sirs) and a handful of barons, but not anything higher than that because the titles of Duke, Earl, Viscount, and Marquis are usually ancient and go back centuries. Creating one of those titles brand new would have required literally huge sacrifices to not only the king but also to country. These titles were often given due to services rendered during the upheaval of war and battles and Kings needed loyal men to hold lands from invaders.
Although not unheard of (the last Earl of England was given to former prime minister Harold MacMillan in 1984), it was extremely difficult to get a title--particularly when land grabs by foreign invaders in England came to an end. The way it is represented in this version of Bridgerton, it seems like hundreds of titles were given to Black folks within a span of 50 years. That wouldn't even be possible for white folks. Charlotte was queen from 1761 to 1818, HOWEVER it is important to note that she was not the regent. Her husband was. Charlotte is more or less powerless, the same way that Prince Philip currently is (husband of Queen Elizabeth, current reigning monarch). They can perhaps lend influence to the reigning monarch, but officially they themselves make no decisions. Of course, there were some royal spouses who were more cunning, but it wasn't the case here.
Perhaps the most famous black person of the British Ton was Lady Dido Elizabeth Belle/Lindsay (1761 to 1804). Born a slave to British Naval Officer Sir John Lindsay and an African slave Maria Belle (West Indies), she technically didn't become an official part of the peerage until upon her Uncle's death, he set her free and bequeathed her a large dowry. But even so, when you read about her life, although it sounds by all accounts that her white relatives loved her, outside society still scrutinized and dehumanized her.
