Google Play Store recent rule change requires all apps to store their data in the app's private internal storage instead of the public internal storage where the CustomMaps directory is. So when the latest Custom Maps version (1.8.1) launches the first time, it tries to copy all the existing maps from CustomMaps directory to the private internal storage. The app assumes that it has the storage access permission, since existing users have previously had to give the permission to create and use maps. Unfortunately, it turns out that Android OS has turned off the storage read permission in many cases, and the Custom Maps app fails to read the existing maps.
To make the Custom Maps app to find and copy the existing maps, you need to long press the Custom Maps app icon, and select "App info" in the pop up menu (or find Custom Maps in the system settings "Apps" section). Then you need to clear all data from Custom Maps (this does not delete maps in CustomMaps directory), and then enable the permission to access local storage. When you launch Custom Maps after that, it will find the Custom Maps directory and copy the maps into the private internal storage. After that first run, Custom Maps will not attempt to access the CustomMaps storage on the emulated SD card (aka public internal storage) ever again.
After the maps have been copied to the internal storage where they are not easily accessible to the user (you), you can use the new "Export all maps" menu item in the maps list screen to make a backup copy of your maps to for example Google Drive. You can also export maps individually from the context menu in the map list, or when the map is displayed on the screen. To open existing map files (with kmz extension) that are not in the internal memory, you can click them using a file manager like Google's "Files" app (Samsung's "My Files" does not work), and it should suggest to you to open the file using Custom Maps.
And the error with map images being too big is caused by an unfortunate bug that fails to use any image files that are named with spaces or special characters in them. If you rename your map image to use letters A-Z, a-z, digits 0-9, and underscore and dash (_ and -) you should be able to open any reasonably sized images without the error message.