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.