I think that by trying to compare the two carpets side by side, each one affects how you see the other. If you take separate pictures showing each sample tucked under the bit of furniture on the right and against the stringer(?), then you can see how each one would look just on its own merits. I have an oak staircase and have something that is more tonally like the one on the left (a tweedy beige / grey / ivory), but my decision was influenced also by paint colours being used.

I’m no colour expert, but I feel a stair carpet like your first pic is very neutral and won’t clash. Ive seen rooms that mix cream, grey and beige and they just look lovely. The dark staircase will add another dimension but still quite neutral. Your staircase is so beautiful it really doesn’t need too much of a change, Skimming Stone is a lovely grey/beige. I would get match pots of the colours you like, paint them on A4, or larger, card and try them in various places and see what you think, paint colours can really change depending on aspect and light. If you can get some carpet samples too you can create a mood board so you can really get an idea of the look. The pics below show how lovely grey, beige and black/grey/brown can look together. Not sure if this is your thing?

I am not exactly sure what kind of shade your carpet is exactly, but these are all great colours to consider. Have a look at the image with the different colour pallets, go with opposites on that, if your carpet is more on the cooler side, choose a shade from the warmer shades and then vise versa. Then for your little boys room, a cooler blue is a nice touch. The picture with the half and half colours, blue and white is also a good touch and will go well with the carpet.

I agree the colour on the seat cushions of the sofa, a sort of oatmeal? Thing is wall paint is cheap but sofas and carpets aren’t, so match them up first.