Sync isn't to be used as backup device it only sync data from original device to other devices. If you need backup you need to follow the Firefox FAQ on data migration to save the data from data lost. Sync isn't a instantaneous update it takes time to sync devices and both device must be on and connect to the same account for proper data sync.

You can possibly use a removable USB drive to transfer personal data. Since this is about two different platforms, you need to be careful.

You can copy certain files with Firefox closed from one profile folder to another profile folder to transfer your personal data. Note that best is to avoid restoring a full profile folder and only restore important files that are safe to restore/transfer.

• bookmarks and history: places.sqlite
• favicons: favicons.sqlite
• bookmark backups: compressed .jsonlz4 JSON backups in the bookmarkbackups folder
• cookies.sqlite for the Cookies
• formhistory.sqlite for saved autocomplete Form Data
• logins.json (encrypted logins) and key4.db (encryption key/primary password) for logins saved in the Password Manager
• cert9.db for certificates stored in the Certificate Manager
• persdict.dat for words added to the spell checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other website specific data (Site Preferences)
• sessionstore.jsonlz4 for open tabs and pinned tabs (see also the sessionstore-backups folder)

Primary location used for the main profile that keeps your personal data (Root Directory on about:profiles).

• C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\Profiles\<profile>
• ~/Library/Application Support/Firefox/Profiles/<profile>
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data