Oops. My elderly, beer-soaked brain: Upon actually reading ALL of your message instead of merely skimming, I see you've already gotten to the INSTALL file.
So. More carefully this time.
I downloaded the tarball, but I'm unsure where to put
it and/or extract it. I tried putting it in its own directory in my
/home directory, then extracting it there, but I still cannot figure out
how to install it, even after reading the install file. I would greatly
appreciate some further advice about how, what, and where I need to
install Frescobaldi 3.1 and associated required files.
For example, do I
need to separately download and install Python 3.8.1?
Type "python3" at the command prompt. If it works, you don't need to install Python 3.
When you type "ls -l frescobaldi" from within the directory where you unpacked the tarball, you may note that it has the executable permissions already set. So, you can try:
./frescobaldi
(Note the period at the start of the line.) If it works, then you've got everything you need, and you can proceed to either the of the following:
sudo python3 setup.py install
python3 setup.py install --prefix=/usr
Basically, just do what the INSTALL says, and if it gives you an error, then start to explore what dependencies, etc are missing.
If I'm installing
on my machine, do I need QtWebEngine? (I can't find that through Ubuntu
Software, either.)
As to the Qt stuff, I find using synaptic ("sudo apt install synaptic") a bit more helpful than the Ubuntu Software installer. Slightly less friendly, but a hell of a lot more informative. For example, searching synaptic for "qtweb" reveals "libqt5webengine5" among other things. That's what you would want, if you don't already have it.