You could express that same relationship in terms of area where the numerical differences would be 2x but the lens/teleconverter choices would be the same. We use the linear form because it is convenient for mental computation, and because it bypasses the human tendency to hear "twice as much resolution" and subsequently multiply a linear value by 2x instead of the area. But the linear form is not resolution. It is a way of modeling resolution and predicting certain things related to resolution. It's no more or less valid than area in your use case.Knowing that resolution varies as the square root of the number of pixels for a given size is very useful practically. Suppose for example that you have a 48 Mpx and a 24 Mpx FF camera. The 48 MPx has sqrt(2) times the resolution, ie 1.4x. This means in practice and all other things being equal, a 500mm lens on the 48 has the same resolution as a 1.4x500mm, ie 700mm, on the 24 Mpx and puts as many pixels on the duck. You know that you have to put a 1.4xTC on the 24 Mpx to give it the reach of a 48 Mpx.

I would say that if you're talking about data captured then it's more useful to treat the sensor as the 2D object which it is. Absent the linear qualification, if you ask me the resolution difference between 24mp and 20mp as a percentage the answer is going to be 20%.

Let's get down to it: this debate exists in general in the photographic community because someone with a shiny new camera with more pixels wants to hear the bigger number (area), while someone who has an older model with fewer pixels wants to hear the smaller number (linear). Which is why I explicitly pointed out that none of this directly relates to human impressions of a photograph. Resolution is relevant and can be important in some circumstances. But there are so many factors at play that you can literally have a situation where a casual observer thinks a 16x20 8mp print is sharper and more detailed than a 16x20 24mp print.

tl;dr - The extra 4mp in the R3 will give a bit more room to crop or enlarge. It's not a dramatic improvement but it is an improvement while still keeping a sports camera fast and file sizes relatively small.