We are using texture brushes
Let us define the concept of texture.
When talking about tactile textures, we usually start with "no texture" or a super flat polished surface.
In visual representations, we can also start with a flat, single-color canvas.
A vector file is a series of descriptions that are reinterpreted when the image is rendered. Let me describe a flat line in an invented vector language:
A Flat line.
Let me be more specific.
A long Flat line.
This can be a very long line. But the description of it is very short.
Now let me add texture to that line.
A wavy line that repeats a wave of x height every 1/100 of the extension of it.
This was a procedural method. I gave the procedure to generate the wavy line. The line itself can be long or short, but the description will remain relatively short.
But what happens when we add a lot of texture, and roughness that is detailed? Imagine a rocky horizon
Add some vertices at this coordinate,
then add some more to this coordinate,
and after that, add another vertice at this coordinate.
We have the description of 1 rock... now multiply that 100x times to have simply 100 rocks.
Can certain kinds of brushes or how brushes are made affect size?
Depending on the concept of texture, a file size of the description of every vertex on a vector file can be hundreds, thousands, or millions of times bigger than an original simple shape.
What should be done to reduce file size in this case?
Export the image to a raster format of the specific size you need it. Normally PNG file or similar. If the texture is very complex, like a watercolor image, that has a lot of inner textures, not only on the outline shape, you can even use a lossy format like JPG.
Take a look at another answer that gives you some reference graphs regarding file size. Why is PDF much larger than PNG for a vector design?
I am still assuming that the information in the file is all vector. Some filters can be raster effects inside the vector file. SVG, PDF, etc. accept raster images inside themselves.
In those cases, this raster file depends on the size the document has declared itself to be. If you are designing on an A4 canvas and it has rasterized effects, try lowering the declared resolution inside the application or reduces the file size to let's say A10, and the raster effects will only render for that size.
What is the usual size that is found for SVGs for web/app usage across the internet?
There is no "usual" anything on the internet. But things try to be low weight when displayed on a normal webpage.
SVG is normally not used to display textured things, but flat things. Logos, diagrams, schematics. You can zoom in on a diagram, but you do not need texture. We normally leave textures to the realm of raster images. (Gradients are not textures, so we can use both)