I have a file manager. And I can do what you are saying about going to saves like you did. That is not the problem for patching.
For patching and modding when dealing with an APK is that usually the place the patch/mod needs to go is a location INSIDE the APK or in a certain folder location on the device that, in newer androids, is secured away from owner access without root access. In older androids, there was a possible way with using a file manager app like Files (Android 10-, some Android 13).
All the people writing mods for this game have either stated without root access, the game cannot be modded on Android 14+ or have provided links to purchasable apps (see installation spoiler
here) that may make it possible.
I'm quite tech saavy (though, I don't play this on android nor do I use the mods) and your process in explaining had been muddied, at best, that I have had to ask for clarifications. I also do not think you are aware where mods/patches actually need to go, based upon our conversation.
If you have successfully patched/modded Summertime Saga in Android 14+, then including step by step instructions for others to follow would be useful. Simply stating to "use Files" and showing screenshots create more questions than answers.
play v.0.20.16 - all the old content is there. Download from the developer's website or OP.
Only play v21.0.0-wip.#### if you want to see the preview of the tech update that is a work in progress, with only minimal content migrated over and small bimonthly releases.