### 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/ProfileWeight.java
private final Weight subQueryWeight;
    private final QueryProfileBreakdown profile;
    public ProfileWeight(Query query, Weight subQueryWeight, QueryProfileBreakdown profile) throws IOException {
        super(query);
        this.subQueryWeight = subQueryWeight;
        this.profile = profile;
    }
    @Override
    public Scorer scorer(LeafReaderContext context) throws IOException {
        ScorerSupplier supplier = scorerSupplier(context);
        if (supplier == null) {
            return null;
        }
        return supplier.get(Long.MAX_VALUE);
    }