C:\>rclone copy atlassian:plugins/servlet/export/download/?fileId=a7307c5e-9d3d-4710-595f-ce6f0d9ec6df C:\Backup -vv
2023/08/04 10:58:23 DEBUG : rclone: Version "v1.63.1" starting with parameters ["C:\\ProgramData\\chocolatey\\lib\\rclone.portable\\tools\\rclone-v1.63.1-windows-amd64\\rclone.exe" "copy" "atlassian:plugins/servlet/export/download/?fileId=7c30a75e-dd93-4071-95f5-6dfce9ec6f0d" "C:\\Backup" "-vv"]
2023/08/04 10:58:23 DEBUG : Creating backend with remote "atlassian:plugins/servlet/export/download/?fileId=a7307c5e-9d3d-4710-595f-ce6f0d9ec6df"
2023/08/04 10:58:23 DEBUG : Using config file from "C:\\Users\\me\\AppData\\Roaming\\rclone\\rclone.conf"
2023/08/04 10:58:23 DEBUG : Assuming path is a file as HEAD response is an error (400 Bad Request)
2023/08/04 10:58:23 DEBUG : If path is a directory you must add a trailing '/'
2023/08/04 10:58:23 DEBUG : Root: https://mycompany.atlassian.net/plugins/servlet/export/download/
2023/08/04 10:58:23 DEBUG : Creating backend with remote "C:\\Backup"
2023/08/04 10:58:23 DEBUG : fs cache: renaming cache item "C:\\Backup" to be canonical "//?/C:/Backup"
2023/08/04 10:58:23 ERROR : Attempt 1/3 failed with 1 errors and: failed to stat: HTTP Error: 400 Bad Request
2023/08/04 10:58:23 ERROR : Attempt 2/3 failed with 1 errors and: failed to stat: HTTP Error: 400 Bad Request
2023/08/04 10:58:24 ERROR : Attempt 3/3 failed with 1 errors and: failed to stat: HTTP Error: 400 Bad Request
2023/08/04 10:58:24 INFO :
Transferred: 0 B / 0 B, -, 0 B/s, ETA -
Errors: 1 (retrying may help)
Elapsed time: 1.0s
2023/08/04 10:58:24 DEBUG : 3 go routines active
2023/08/04 10:58:24 Failed to copy: failed to stat: HTTP Error: 400 Bad Request
Thoughts
My suggestion is that rclone does not pass parameter fileId in url string which is after question mark. It is based on running rclone with adding --dump=bodies --retries=1 --low-level-retries=1 --log-level=DEBUG parameters to command line. I see in debug that Atlassian responds with error page which states: fileId parameter must be specified.