My Photo Stream is complicating things, as it only transfers the still frame of the Live Photo. It cannot transfer any video at all. With My Photo Stream enabled you cannot transfer the Live Photos alive. I would not use my Photo Stream at all, if you are having a modern iPhone and want to shoot Live Photos. My Photo Stream has not been updated to support the new iPhones well for many years. Apple is not even allowing new users with a new AppleID to enabled it. See: My Photo Stream - Apple Support
"... If you recently created your Apple ID, My Photo Stream might not be available. If My Photo Stream isn't available, use iCloud Photos to keep your photos and videos in iCloud."
Photo formats that you can use with My Photo Stream
"My Photo Stream supports JPEG, TIFF, PNG, and most RAW photo formats. My Photo Stream doesn't support video or Live Photos."