Peter has stopped smoking recently/ in recent days. "stopped smoking" is fine but 'quit smoking' is more commonly used.
Is it a must to use 'present perfect' with 'recently'??? No. In fact I would not use present perfect with "recently". Just say, 'She stopped smoking recently.' But without a time word like "recently", you can say 'She has stopped smoking.' (or just, 'She stopped smoking.')
Is 'in recent days' correct here? I wouldn't say that; it sounds very unnatural. If you want to mention "days", say 'She stopped smoking in the past few days'.
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