Hi Martin,
Actually, there is no direct URL for generating the report file.
When we click the Usage button in Popularity and Search Reports, the button will call a JavaScript method to send the request to the server and the report file will be sent back as a response.
And it seems that there is no such API for getting the reports in Client Object Model, so you need to do this one by one in the site collections in SharePoint Online.
Thanks,
Victoria
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