Programatically define RequestMappings for a custom Spring Boot starter

Question

I'm trying to create a Spring Boot starter project that defines controllers programmatically based on the existence of certain types of beans. In the auto configuration class I defined a RequestMappingHandlerMapping where I register the handlers programmatically similar to the following:

@Bean
public RequestMappingHandlerMapping customRoutes(ApplicationContext context) {
    var handlerMapping = new RequestMappingHandlerMapping();
    findTargetBeans(context).forEach((name, bean) ->
        var getMapping = RequestMappingInfo
                    .paths("/" + name)
                    .methods(RequestMethod.GET)
                    .produces(MediaType.APPLICATION_JSON_VALUE)
                    .build();
        handlerMapping.registerMapping(getMapping, createHandler(), getHanderMethod());
    );
    return handlerMapping;
}

This seems to build just fine, but when I try hitting the registered paths, I get a 404 response. Am I missing something? Do I need additional configuration to make this programmatic routing to work? I've been looking at old questions like this one, and this one, but none of the answers work for me.