At the moment it is possible to retrieve the count of work items retrieved in a JQL via lookup issues component. The problem with that is that this component has its own restrictions like looking up more than 100 work items while at the same time loading their fields, etc.

With the new addition of this REST API endpoint here: https://developer.atlassian.com/cloud/jira/platform/rest/v3/api-group-issue-search/#api-rest-api-3-search-approximate-count-post it would be easier to retrieve only the count of work items returned in a given JQL without hitting the service limitations.