I am not an electrical engineer but as far as I understood the article at hackaday the reason is not a battery too old it is the so called 'security' Sony built in. I tried it with two batterys as stated above and have the same issue with both. So I will try to solve it in the way as described at hackaday.
This so called 'security' mechanism is built in nearly everything that needs batterys and other 'perishables'. I know it from printers (ink cartridges), from cameras (battery), ... The producers are building them in to a lot of electronic parts to prevent users from using 3rd party batterys, cartridges, etc. They tell us that this is to prevent issues but in reality this has a commercial background. Never had any issues with 3rd party batterys or cartridges when they build in a chip to overcome such 'security'. But in the case of the PRS-950 it seems that there is no such chip built in to the battery and therefore this issue happens.
As an example for this:
https://forums.theregister.co.uk/for...c_battery_drm/
Sony also is doing it:
https://www.sonyalpharumors.com/new-...rty-batteries/
Indeed the way of the implementation is different but the result is the same: You cannot use the 3rd party battery as spare part!