The other pins can be a temperature sensor or data. If data (SDA & SCL), then it's rarely compatible, then a CPU in the cell (or battery pack on a laptop) measures everything and reports. Only some laptops use the same data protocol.
Phones and simple gadgets usually use just a temperature sensor, or nothing in the pack if it's a bag (then something is usually in contact.).
The Kindle Keyboard cell box has a LiPoly bag glued inside as well as a CPU and other circuitry. I'd be sceptical that charging works at all with any other pack. The cells are on eBay, perhaps you need someone else to order.
The problem is that some postal authorities don't allow posting of bare Lithium cells. Technically the Kindle cell is not "bare" as it's in a box with electronics. Though very thin aluminium sheet.
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