This should be the battery needed:
https://batteryint.com/products/3-7v...ire-plug-tools
I personally wouldn't want to spend any money at attempting to fix the device at this stage as I wouldn't be certain it is the battery, but I would want to rule the battery out. It should be simple to do with a plastic pry tool to open the case and a multimeter to test the battery.
With the back of the device open you'll also have access to the microsd which you could test.
If the microsd is faulty, some have had luck in copying an image of the firmware to a new microsd.
If you need a copy of the microsd image for your device you can request it here:
https://www.mobileread.com/forums/sh...d.php?t=355778
To copy the image to a new sdcard:
https://duckrowing.com/2022/02/11/ex...ra-hd-storage/
or,,,
https://yingtongli.me/blog/2018/07/29/kobo-sd.html
You can do this on a Mac or Linux PC... if you only have Windows you could create a Linux boot usb for this task.
A mobileread thread where you may be able to ask for assistance with the microsd:
https://www.mobileread.com/forums/sh...d.php?t=313468