As in title, preferably open-source, but doesn’t have to, I will start:
KOReader - Amazing reader app, and being able to use the same app across various devices, even non-android ones, is pure bliss. Japanese support is pretty good too, which makes me happy. Though… Sadly no vertical text support :c
Syncthing-fork - Being able to keep a library of books, and some files, and easily keep the shared folder across various devices, is mega comfy. Tachiyomi - Cute manga reader.
NewPipe - Really pleasant youtube client, that i sometimes use to listen to things in the background.
Kaku - An useful Japanese OCR app, that works… quite decently for when I encounter kanji that I do not recognize, and is not text.
EinkBro - A web browser, that on e-ink devices, is quite comfy. Has few… quirks, but works well on e-ink
If you absolutely must get something from Google Play, I suggest Aurora Store, which acts as an alternative frontend for Google Play, so you don’t have to have GApps installed.
If you have use for command line programs, Termux, a terminal emulator, is a great option, and it also works with root.
For reading eBooks, I also have a recommendation, Librera Reader (but I’ll check the OP’s recommendation too).
Material Files and Simple File Manager are great file browsing tools. But if you need a file browser for root specifically, I recommend Material Files specifically.
Good list, but termux isn’t a terminal emulator. It’s so much more. It’s like a virtual machine running cli linux with it’s own repos and all. You can have python, gcc, vim, emacs, zsh… you name it. As long as it is tui, it is probably on termux!
Oh yea, Forgot to list Termux, but, since my 10.3" inch e-ink tablet broke, I haven’t been using it as often :c Using emacs inside it, and having lisp… was mega comfy