Unfortunately the dedicated replacement battery is dead. I do not recommend buying it. Before finding that one I had already bought online the Nexus battery. It was a hassle to replace the charging board, but I managed, works perfectly!
I tested the batteries by opening youtube in the built in browser, watching an old movie
https://www.youtube.com/watch?v=h9c1T-ZukQA
The dedicated replacement battery consistently died below 50% at about 30 minutes of the movie.
The Nexus battery also loose charge quickly watching the movie, but it holds well till the end.
It's really subjective, but it feels like the reader is working noticeably faster with the Nexus battery.
I've never watched movies on this tablet before so I have no idea if the 1h of playtime is a good result or not. At least the Nexus battery behaves consistently. I guess the e-ink draws much more power than a typical IPS display on a phone when it's continually updated at max refresh rate (I think it can get up to 20 fps).
Well, I'll see if I can use it again for a whole week without charging for a basic reading.