That's cool. Looks like Inkscape supports adding this kind of noise through its various effects in its Filters menu. Exported as a Plain SVG and looking at the code confirms the use of feTurbulence.
For comparison, I also did a test to see how Affinity Designer 2 does it, since it has noisy fills. The SVG it exports has the noise embedded in it as a base64 jpeg image!
I'm currently away from my PC so I can't check myself, does it embed a single noise texture and use it multiple times, or does it generate a texture for each use of noise?
As someone who can't justify an Adobe license and can't wrap their head around InkScape, Designer has been a perfect alternative bar quirks like this.
For comparison, I also did a test to see how Affinity Designer 2 does it, since it has noisy fills. The SVG it exports has the noise embedded in it as a base64 jpeg image!