There is no way to sync from website to app yet. Hopefully it will be added into future versions. You would have needed to back-up your old apps and restore them on your new iphone i think.
In fact if u are the IT type, and seriously determined to get back your datas from web to iphone, u can do it by importing it into sqlite db file. But it takes some database updates etc. I used oracle but probably any will do.
Getting log from web to new iPhone
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