Termux first needs the phone to be rooted to properly interact with anything outside of its $HOME, including Android's user's internal storage and SD card

this is false, termux does not need root for most things including accessing internal storage (/sdcard)

Termux is a Linux distro heavily adapted to work as an Android program, but that makes commands familiar; if you used Debian, Ubuntu, Mint, etc., commands follow the same structure as apt's, but using pkg instead

this is also not true, it's not a linux distro, it's just *nixy tools natively compiled for android. thus for example it uses android native libc. apt command also still works on termux, as pkg is a wrapper around apt.