The topic is sending wishes to people on the occasion of the beginning of a new year, the coming year, the 'New Year'. I do use capitals in this context. It is 'next year', but it's unusual to hear best wishes for 'next year'. (I agree about 'the next year' being wrong in BrE) 'All the best' is a formula and is short for 'all the best (to you ... More @Wikipedia
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