How can I change the brush design so that instead small circles there are small squares ?

The Texture Splat brush preset uses a predefined brush called splat_dots which is included in the Krita_4_Default_Resources bundle as splat_dots.png. This is only accessible when krita is running.

If you feel comfortable about digging into krita's system storage area and extracting it from the bundle you can do that and then edit it to make the round dots more square and thus create your own 'egart_splat_squares.png' brush that you can put in your brushes folder in the standard resources area.

Or, you can make your own 100 x 100 .png file from scratch and use the Texture Spat brush preset as a stamp to place the splat_dots brush image on the canvas then edit it to make the dots more square, or anything you like.
To do that, first you'd need to go into the brush editor and turn off the Size, Rotation and Strength parameter controls so that it behaves as a simple stamp instead of a complex brush preset.

Making a good looking brush image is not easy so please get back and post the results when you're finished and satisfied with it.

It might be easiest to create a new brush with the spray engine, which supports square splats by default.

I tried the spray engine with squares and it is possible to get something similar in terms of density, size and scatter but it doesn't give the same overall 'look and feel'. I may not have tried hard enough or for long enough.

For modifying splat_dots using a new image from a stamp, I tried it quickly and I left some fading at the edges to make the squares less harsh. It needs a bit of cleaning on some of the edges.

https://i.imgur.com/cNJyr8F.png