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While this doesn't directly answer your question as the endpoint is not returning a literal count, but below is a possible work-around:
To limit the amount of data returned, you could add '&fields=(id)' to help speed up the query.
Manually count the results returned.
Hope that helps,
If not possible, this might warrant an idea (Although I like Bryce's workaround). Because of our lack of ability to filter out content created by Rest API calls (and the bigger reason of turning on SSO), we have restricted our employees from making Rest API calls. If people have needs for APIs, we run them with service accounts, which of course gives us an easy filter (by account).