I'm not sure about the PRS-T3, but later versions of ADE (2.0/2.0.1/3.0) have a bug that prevents them working with Sony PRS-350 and several others in conjuction with Overdrive library books.
Adobe have been aware of this bug (and many others) on ADE 2.0 for over two years, but don't seem in the least bit interested in fixing them.
ADE 1.7.2 works fine.
Thank you for the answer. I feared that much, since the T3-model was not in Adobe's list over compatible products. I hoped it was simply because the list was too old, but it seems there is a different explanation to that.
A different question: my old reader was authorised in ADE. Can I bind a new (and compatible) device to the same ID so I can continue reading the books I have already purchased with the old ID?
You can register up to 6 devices at a time with a given Adobe ID.
Sometimes the Adobe system doesn't notice when you deregister a device, or you lose access to a device without first deregistering,
You then have to contact Adobe service (live chat) to get all the registrations reset and start registering again the ones you still want.