Apologies, the documentation for this is lacking (I will update it now). The name of the param for custom-html is content.
We don’t have anything ready-made for the full /latest list, but you build your own and add it to the configuration using its name. Should be very similar to the category/tag lists, just without a filter.
Currently, no, you can’t show it on specific categories only. You can however use discovery.category in the show in routes setting, that will only show the sidebar on category routes (but on all of them, not a subset).