I would read "papers" as different from email. Papers I interpret as personal records: journals, financial records, etc. Email, tweets, Facebook postings, etc. are already by default shared with at least one other person or unknown other persons so there's an implicit reduced notion of privacy.
I agree with the larger point that information on digital devices should properly be considered "papers" or "effects" even if stored in something nebulous such as "the cloud." As long as there's no deliberate or implicit sharing of these things, "the cloud" should be considered as private as a desk drawer.
Financial records are also shared with others. And my correspondence with another person is also private whether achieved via paper and envelope or by email or instant message.
I agree with the larger point that information on digital devices should properly be considered "papers" or "effects" even if stored in something nebulous such as "the cloud." As long as there's no deliberate or implicit sharing of these things, "the cloud" should be considered as private as a desk drawer.