I have a Kindle Touch 4th generation. It is 12 years old. Working but the battery is only a few hours in standby mode.
I bought a replacement battery on Tmall.com. Chinese Yuan 36.
The very first step is to open the case of Kindle Touch.
I followed the video to open the back cover of the kindle.
It looks like below.
Remove five screws to take down the battery.
Install the new battery.
Put the back cover on.
Charge it until full.
Now, I feel it is good for the next five or more years.