When I first started using the local library (Balham Library, in London), about 40 years ago, I recall:

- the book had that paper thing with dates stamped on it

- I think there was a pocket, but that the librarian emptied the pocket before handing me the book

- the librarian scanned a barcode on both the book and on my library card, during checkout (using a pen-like scanner)

Perhaps I'm mixing memories from different times. Or perhaps I joined the library soon after it was computerized. Perhaps the backend was computerized but they still did the date stamp thing because that was the only way I'd know when the book was due back.