Is the telescope design available anywhere for hobbyists to build? I can't seem to find anything in the article or in a separate search. I'd be interested in perhaps putting one of these together to do radio astronomy with my kids.

Maybe you like this:

https://physicsopenlab.org/2020/10/10/a-simple-11-2-ghz-radi...

The HN discussion (2020) about this can be found there:

https://news.ycombinator.com/item?id=26078761

I couldn't find the link that they mentioned too. Maybe they forgot to actually put it?

Search on “diy radio telescope”, that gave me lots of projects and videos

edit: It looks like NASA is back selling Radio JOVE kits again. So this might be your only turnkey choice. It uses 2x large wire dipoles for 20.1 MHz for receiving Jupiter/Io radio bursts which you just view in a spectrogram on a computers (includes SDR receiver): https://radiojove.gsfc.nasa.gov/kits/

I think the SETI "Horn of Plenty" design is a pretty good way to get started with kids. The antenna itself uses metalized foam board with copper (or even aluminum tape) to make a pyramidal horn. Making the waveguide out of folded aluminum siding is a bit more kid dangerous (tin snips cutting sheet metal). And the actual antenna is a monopole feed placed in the waveguide. You'll still probably need an cheap ebay low noise amplifier, less cheap hydrogen line bandpass filter, a SDR receiver with a couple MHz instantaneous bandwidth and a computer. Cheap RTL-SDR usb receivers aren't great at 1420 MHz but they do work if you have a good filter. You'll have to decide on the receiver based on the processing toolchain you chose and it's requirements. Examples using GNU Radio https://github.com/ccera-astro or https://wvurail.org/dspira-lessons/

The "science" output of this isn't very exciting to kids as it's just a spectrum plot for a point in the sky at the time showing how fast towards or away from us some of the hydrogen is going. But if you do it over many full sidereal days at different elevations and record the elevation w/time then you can make a nice looking "image" of the sky showing something useful.

If your kids are older and ambitious take a look at the STARE2 project for detecting fast radio bursts which does actual honest to goodness publishable (https://www.nature.com/articles/s41586-020-2872-x) radio astronomy with a meter scale horn+receiver setup. https://www.caltech.edu/about/news/magnificent-burst-within-... https://arxiv.org/abs/2001.05077 The secret sauce of STARE2 is math heavy calibration though.