The ILL section in the manual points to this wiki page https://wiki.koha-community.org/wiki/ILL_backends which needs a serious cleaning and update Or maybe the list of backends maintained by vendors could simply be added in the manual ? The manual already makes references to one of them (Britsh library)
In various git repo I found backends for British Library, Libris , INN-Reach, RapidILL , Rapido, Reprintsdesk, IncDocs