Your setup is not clear. Did you backup to one drive, or only sync one drive? If you sync’d do a manual sync on the old computer.
for emails, probably you stored some locally, rather than on the email server. If you still have the old pc, map the local folder to one drive, and do same on new pc. You can also move the local messages to folder on the email server. If the the local folder was backed up and restored on the new computer, you just need to map.