Not using the same resource pack as OP, but encountering basically the same issue (and I have too in the past). In my case, the subpack sliders does not even show when opening the resource pack within the realm. Downloading de realm, changing the world_resource_packs.json and replacing the realm again does not resolve this, the resource pack goes back to its original setting. Everywhere else, the resourcepack works fine, this is deifinitely a realm issue, which needs to be addressed.
Not using the same resource pack as OP, but encountering basically the same issue (and I have too in the past). In my case, the subpack sliders does not even show when opening the resource pack within the realm. Downloading de realm, changing the world_resource_packs.json and replacing the realm again does not resolve this, the resource pack goes back to its original setting. Everywhere else, the resourcepack works fine, this is deifinitely a realm issue, which needs to be addressed.