Are you using SwaggerFeature plugin or OpenApiFeature plugin? And what version of ServiceStack are you using? In recent version 4.5.13 which is available on MyGet Apis are sorted in alphabetical order.
Yes, this is the version of OpenApiFeature plugin where operation paths are sorted alphabetically by default. If you didn’t redefine serialization routine for OrderedDictionary you should get similar picture.
The Swagger UI controls the ordering which does initially group by path segment which is why you’re seeing all your APIs under the api group, but doesn’t appear they order within that group.
You could try reordering the APIs in the ApiDeclarationFilter where you can try reordering the Paths OrderedDictionary where your APIs are defined which may have an effect in Swaggers UI.