"though in such a case the limiting factor in developing such a weapon is not usually design difficulty but rather the procurement of material (enriched uranium)"
This paragraph refers to the simpler-to-design gun type (eg Fat Man). According to WP the three PhD guys designed a much more complicated implosion-type bomb within only 3 years with public information and only basic tools.
Fat Man is the “much more complicated” design and the guys picked it because it is more challenging.
Results of the analysis are still classified (declassified document is redacted to death) but there are some accounts claiming that Dr. Teller uncovered that the design was viable and would produce a blast within order of magnitude of the “inspiration”.
If the account above is true it means anything from low single digit kiloton range to low double digit.
But I do not think today anybody would doubt that. The biggest obstacle to fission bomb making are materials themselves. Lack of public data to calibrate would mean nothing to terrorists (1 kiloton is still terror-inducing) and nation states have no problems in accessing nuclear scientists.
Fortunately, getting enough material is what makes this lunacy impractical.
This begs the question: Is it illegal to design a nuclear weapon? Or any weapon for that matter, sounds like hell of a hobby. Could you outsource a modern day Kalashnikov to the third world through the daily Slack and Zoom?
Not really, there is a big framework of regulations designed specifically to make that not a thing - from international treaties to local laws. They cover all sorts of things including the materials, the development and trade of adjacent and dual-use technology and industrial capacity, etc.
Not quite but closer than you might have thought, see
https://en.wikipedia.org/wiki/Nth_Country_Experiment