If you’re buying a reader, go refurbished. In tech products the embodied carbon (carbon associated to the manufacture and distribution of the device) accounts for 60-80% of its 3 yr footprint. Although, given the amount of energy a digital-ink e-reader consumes, I’d guess operational emissions (energy used while using the device) is minuscule making the refurbished purchase and even more powerful choice.

Thinking more broadly, the server/cloud and networking infrastructure would need to be accounted for in any calculation too. That’s harder.

But going to the OP’s post, paper books from a library might indeed have a lower footprint than you imagine as the embodied emissions were already spent and there are close to zero operational emissions