A composable index template with no `template` defined in the body is mistakingly always assumed to not be a time series template. Even if it refers to a component template that has the `index.mode` setting set to `time_series` and the component template defines mappings with dimension fields or routing paths.

Incorrectly this causes to create a data stream with a tsdb index *without* time series start and end time settings set. The fact that this can happen is another bug and is being tracked #98833.

What should happen in this case is that a tsdb data stream is created with a valid tsdb backing index (with correctly generated time series start and end time settings).

This bug was found as part investigating #98792 and is the cause of that bug.
server/src/main/java/org/elasticsearch/cluster/metadata/Metadata.java
if (indices == null || indices.isEmpty()) {
                throw new IllegalStateException("Cannot remove non-existent alias [" + alias + "] for index [" + index.getName() + "]");
            }
            indices = new HashSet<>(indices);
            if (indices.remove(index) == false) {
                throw new IllegalStateException("Cannot remove non-existent alias [" + alias + "] for index [" + index.getName() + "]");
            }
            if (indices.isEmpty()) {
                aliasedIndices.remove(alias); 
            } else {
                aliasedIndices.put(alias, Collections.unmodifiableSet(indices));
            }
            return this;
        }
        public Builder put(IndexTemplateMetadata.Builder template) {
            return put(template.build());
        }
        public Builder put(IndexTemplateMetadata template) {
            templates.put(template.name(), template);
            return this;
        }
        public Builder removeTemplate(String templateName) {
            templates.remove(templateName);
            return this;
        }
        public Builder templates(Map<String, IndexTemplateMetadata> templates) {
            this.templates.putAllFromMap(templates);
            return this;
        }
        public Builder put(String name, ComponentTemplate componentTemplate) {