Starting from Android 13, the default external storage won’t work. However, it allows scoped storage, enabling you to save game files within the data folder of the game without requiring any additional permissions. Please note that the Play Store will also reject apps targeting Android versions below 13, so updating is advisable.
I’ve faced a similar situation where the save game code is embedded within the engine code, making it impossible to directly modify the code to change the save path. The only solution I found was to update the engine to UE5.3, which saves the files inside scoped storage. I’m not certain if this solution is suitable for your situation, but it worked for me.
Someone suggested editing the path of the saved game with cloned version, but I have the launcher version so couldn’t try out.