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OK, I've Backed up Contacts & all other items using Samsung "Smart Switch", see this link :-
As a Mail Service I use "Thunderbird", no idea whether that Sync's
That's the client (the program that collects your messages). The service that would sync would be the email provider, eg Gmail, Yahoo etc.
Yahoo will store contacts if you allow it to. For information on syncing with a mobile device, have a look at the website.
You may also be able to sync your contacts with Google even if you don't use Gmail. If you have a Google account and have signed in on your phone (you'd need to in order to use Google Play), you may find that this is happening already. When you try to export your contacts (as I explained before), if the account offered is your Google identity, it's happening.