Not to be pedantic, @calicogoose , but the NT link says it is unknown as to whether the child is a depiction of an actual servant owned by the family or meant as a symbol of slavery. There is more than one possible way of looking at the painting, and it is open to interpretation.
Either way, real or symbolic, the child represents slavery in Britain because there would have been no other way for a small Black child to be in 18th century Britain without being a slave.
I'm sorry, but that is 'bleeding obvious', as I've said before. No matter what your education was like or how old you are, it is a matter of general knowledge that Britain's indigenous population is white-skinned, so anyone not white-skinned has to have come here from somewhere else originally. It is also a matter of general knowledge that Britain was heavily involved in the slave trade in the 18th century. I don't think the NT is asking a lot from visitors to make that connection themselves.
I used to volunteer in a NT property behind the scenes many years ago and the reality is that:
a) Individual properties have widely varying budgets for things like displays and labelling, and often have to make very difficult choices about where their money goes - conservation has to be the priority in many properties
b) The curators of NT properties have a huge amount of responsibilities beyond the collections in the buildings. Expecting them to have an encyclopaedic knowledge of every object on every surface in the home they manage is utterly unreasonable. They do their best, of course, but some properties have tens of thousands of objects contained within them.
Your other points about NT properties attracting less diverse populations than London galleries are a little misleading, as you suggest this is proof they are unwelcoming to people of colour. London is the most racially diverse part of the UK. So of course you're going to find a hugely diverse group of people visiting - it's on their doorstep. Most NT properties are situated in rural parts of the UK where the population of people of colour is very low. Less than 20% of the UK population is non-white. Most of this population is centred around the big cities. So on an average day in an NT property in the middle of, say, the Somerset countryside, no, you're probably not going to see any people of colour visiting. Is that because they don't feel welcome? Or is it just because there are so few people of colour living in the area?
I do take umbrage with your insistence that the NT is doing a terrible job of representation because I don't think it's true. Many of their properties have done a thoughtful and considered job of telling the stories of their difficult pasts over the past decade, and there are numerous and regular initiatives to encourage and welcome visitors from a wider range of backgrounds. Nowhere is perfect, but you using one example of a painting you felt was badly displayed to write off a whole organisation's dealings with slavery is more than a little unfair. I think you need to go and see some other properties and how they deal with similar pasts before you make such sweeping judgements.
I also think some onus has to be on visitors to educate themselves. If I'm going somewhere for the day, I will look it up and find out some information before I go, so that I have a base of general knowledge that I can then use to find out more once I'm actually inside. If I can't find out what I want to know from a room guide, I'll take a photo and then look it up myself when I get home. I don't expect to be 'told' everything I want to know, just as I don't expect everyone in the property to know everything about everything on display.