### Description

As we are about to start leveraging `Weight#count` to compute total hit counts (https://github.com/elastic/elasticsearch/pull/84778) and aggregation counts (https://github.com/elastic/elasticsearch/pull/81322), we should start instrumenting it so that we can get information about time spent in `Weight#count`.
server/src/main/java/org/elasticsearch/search/profile/query/QueryTimingType.java
/*
 * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
 * or more contributor license agreements. Licensed under the Elastic License
 * 2.0 and the Server Side Public License, v 1; you may not use this file except
 * in compliance with, at your election, the Elastic License 2.0 or the Server
 * Side Public License, v 1.
 */
package org.elasticsearch.search.profile.query;
import java.util.Locale;
public enum QueryTimingType {
    CREATE_WEIGHT,
    BUILD_SCORER,
    NEXT_DOC,
    ADVANCE,
    MATCH,
    SCORE,
    SHALLOW_ADVANCE,
    COMPUTE_MAX_SCORE,
    SET_MIN_COMPETITIVE_SCORE;
    @Override
    public String toString() {
        return name().toLowerCase(Locale.ROOT);
    }
}