Categorisation of Harmonised System codes for economic analysis
If you are looking for classification like Agri-food trade presentation that covers products other than agricultural, you should check out the Combined Nomenclature (CN) of the European Union and its Explanatory Notes.

It is established on the basis of the Harmonized System and it covers all the products that can be subject to customs and tariffs in the EU. Seek Annex I to the the basic CN Regulation (Council Regulation (EEC) No 2658/87 on the tariff and statistical nomenclature and on the Common Customs Tariff). Be sure to use the latest version, though, as it is updated on a yearly basis. Here's a link to 2018 version, but if you want to be accurate, you should also include amendments (there were five of those since publication of 2018 verion). Perhaps the most readable is of course Explanatory Notes to the CN (so something like this).

If you are interested in jurisdictions other than EU, please find links to cusoms nomenclature under Harmonized System's wikipedia page, you've posted. I'm sure all of them will have the same problems as Harmonized System. It is simply impossible to explicitly list all the products in the World and such listings will always be half open with use of phrases like 'not elsewhere specified'.

Hope that helps.