I've tried in the past but some dont work with how I have my files set up. I use secure folder (for obvious reasons) and it didn't work for me when i tried before. I'm aware at this point it's kind of a me problem but it's still annoying, and for ease of access purposes you shouldn't need install a separate file manager to install it. Just making it known just in case the devs were unawares. If they are planning to continue this way they should put it somewhere in with the installation instructions that you are gonna need a third party file manager in the case you're using a newer android device. That, or figure something else out. I'm pretty sure they do it this way because of the 2GB limit on the apk format, which can be solved by breaking it up and formatting it as separate installer apk packages. That's what a lot of indie VN developers do to my knowledge. It's not perfect but it's better than them not addressing it which is essentially the same as saying "figure it out for yourself". Which seems a bit lazy, intentional or not.
Renpy doesn't support creating multiple apk's. It only supports a single apk, which you correctly stated is above the 2gb limit. The install instructions on the wiki tell you that a13 has permissions requiring a 3rd party file manager such as zarchiver.
If you are aware of a way to take an existing apk and split it into multiple then that's something that can be looked into. But as far as I'm aware the only other option is to have people move the assets into android/data as they are now.
Where as im uncertain whether the game itself was made entirely in renpy or unity, "Out of Touch" i guess would be a good example. I criticized it before given how tedious it was but after understanding the 2gb apk limit I changed my tune. They took all of the asset files, and split them up into different apk's that just acted as installers. You'd basically just install all the assets with the installers, then install the main apk that runs the game itself. I'm not sure entirely how they did it, whether or not it can be done with renpy. I would assume so since it's just simple python code telling it which files to install where, and coding install and uninstall buttons. If it can't be done in renpy directly, python is basically the same language since renpy is based off of it, you could just do it there. Again, I'm not an expert its just hypothetical nonsense. Also whether or not it's on the wiki saying to use a file manager means nothing. As far as I'm aware, it isn't stated anywhere on itch, so anyone trying to install from itch has to "figure it out for themselves" as I've stated before. I have huge respect for VN developers and the amount of effort they put in to these games. Just figured I'd throw some ideas to the wind since I feel the current setup is inconvenient to some of your target player base. Better to take the extra step to be all inclusive then leave out a portion of people because it's easier, no?
OOT was a renpy game converted to Unity. Unity likely has an option to allow for creating multiple APK's or can be created. Renpy compiles your apk and only has an option for one, meaning there is no way to make 'installers', without modifying Ren'py (and the RAPT compiler) internally. Unity doesn't run on python, its C#, and Android permissions are a lot more complicated than a simple install or uninstall button. Could it be done? I'm sure if you wanted to mess with it. Would a single Ren'Py update break everything horribly? Almost certainly. I wouldn't even know where to start with having something like that. It would be easier to make a full on launcher style app for Android, and even that isn't easy.
The install instructions are inside the Android zip file, so anyone who downloads has instructions on what to do. I wish it was easier, and I know some people struggle, especially on Android 13. But short of programming a custom solution, there isn't an easy fix. I would be curious to know how the game who's name I'm forgetting works, since they were able to move the assets to a different directory. That could be something that is looked into