Issue
If you're using the authentication Microsoft_Modern or Microsoft_Modern_Admin, the file size limit for up- and downloads in the Cloud Connector is 2 GB.
Explanation
With the Microsoft_Modern authentication, which is recommended by Microsoft, it is not possible to download files larger than 2 GB. This is a limitation of the Microsoft SharePoint libraries that the Cloud Connector utilizes for the synchronization.
Because of this limitation regarding the download, the Cloud Connector also prohibits uploads larger than 2 GB to ensure that the data entities can be kept in sync.
Detailed Technical Background
SharePoint does allow uploading up to 250 GB (since March 21, 10 GB before that) through its web interface, the OneDrive for Business client, and their SharePoint migration tool. However, this is not possible for 3rd party software due to the following technical limitations:
Microsoft recommends using what they call "Modern Authentication" which we provide in the Cloud Connector as "Microsoft_Modern". This is essentially an OAuth 2.0 based authentication. We use the Microsoft Active Directory Authentication Library (ADAL) to retrieve an OAuth 2.0 access token, which we then inject into the CSOM communication.
The OpenBinaryStream method of the File class in the Microsoft CSOM libraries is used for file download. This fails with the error 'Invalid MIME content-length header encountered on read.', which is thrown in the constructor of the Microsoft.SharePoint.Client.Mime.ContentLengthHeader class. This is due to an attempt to parse a string-representation of the number of bytes to be downloaded into an integer value, which can only represent 2 GB at most.
We could upload / download up to 10 GB through pure HTTP, thus bypassing the limitation of calls through the API. However, this is not possible when using Modern Authentication, since you get an access token which only permits API calls.
So, the combination of the Microsoft recommended authentication method and the SharePoint API limitation limits the download in the Cloud Connector to a maximum file size of 2 GB.