I think it's probably just hardcoded directly into the Steam client. I haven't seen anything that would deliver category or genre names to the client dynamically. It looks like you can get category names from HTML on the search page under "narrow by feature" (e.g. I see data-param="category2" data-value="50" data-loc="Additional High-Quality Audio"
Of course, Steam Workshop is on there twice with IDs 30 and 51, because Valve...
Looks like category2 and category3 are both using the same shared "category" values. category1 likely is as well.
I haven't seen anywhere on the store site that directly lists genre IDs, but at least there's not too many of them to figure out individually.
Product info is internally delivered as VDF, which doesn't have any concept of lists/arrays. So when Valve needs a list of values, they sometimes just encode it as "intended_value" "1"
Valve is really good at creating systems that don't return output at all deterministically.
Welcome to the adventure of dealing with Steam.
