If I download an update on android, do my saves automatically transfer or do I have to do something myself to keep my saves?
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Well, you will only lose your saves if you delete the app instead of installing the new apk as an update on top of the previous install.
If the update fails, it's often due to storage space, android is weird and likes to have 2-4GB of free space to install a 1GB app.
Either way, you can make a backup of your saves if you use a file manager that can access the folder (most don't in android 10 and later)
So get something like SolidExplorer or X-Plore and go to.
Android/data/com.domain.corruptedkingdoms/files/saves
Grab the files there and copy them somewhere else.