Back to Zero: (Revert to Unadulterated 9.0.1 Trisquel Etiona?)

As a veteran of frequent reinstalls of Etiona, here's what I generally do:

1. Check the "view hidden files" box in the Caja menu, then navigate to "Mozilla" in the
/home/username/ directory.

2. Copy the contents of the folder /home/username/.mozilla into its own folder in HDD;
the relevant data will be in the "abrowser" subfolder under /home/username/.mozilla. You'll
need to copy some of that data back to your fresh install of abrowser later on, perhaps
with others' help.

3. In the terminal, type "blkid" and make careful notes (if you can't print the output of
blkid) of the specific sizes, locations and UUID's of the various partitions. These data
will be important when you are faced with the choice of target location of the reinstall of
Etiona. Double check by installing GParted and then opening GParted to see whether /dev/sda
and /dev/sdb are as you expect and as blkid says. GParted will also tell you the sizes and
functions of the various partitions in each storage device. In my experience, the identities
of /dev/sda and /dev/sdb may be dictated by the order in which they come to be recognized
during bootup; your SDD may get booted up first and wind up as /dev/sda or vice versa,
contrary to your expectation based on the relative physical locations of the two drives.

4. Reboot into the Etiona flash drive or live DVD; after choosing the install Trisquel
function, navigate through the various steps of language, keyboard, time zone, etc. until
you arrive at a multiple choice menu. "Something Else" is the appropriate selection.

5. You'll be presented with what looks a lot like the GParted table listing all the
computer's drive partitions. Check just the target partition that you've identified beforehand
as the present Trisquel operating system's site. Mark that site for the new installation;
also mark it as root (/) by clicking on the "change" menu item right below the listings of
all the partitions. I had a lot of trouble with this step in the past because it's not at
all obvious to the uninitiated. Once you've successfully reached this step, you'll find that
clicking inside the open area will bring up a list of selections; among them is the absolutely
necessary "/" designation.

6. At the bottom of the same GParted-like page is a place to select what the boot drive should
be. That will be pre-selected for you by the installation media; it's where GRUB will be located:
always in the primary storage media, /dev/sda in my experience. Change that at your computer's
peril.

7. If you have succeeded in making these two selections (home and boot) the installation will
allow you to proceed.

8. If you're at all hesitant to allow updates of the software to proceed in parallel with the
installation of Etiona, deselect "Enable WiFi" and/or "Enable Networking" to prevent the
concurrent updating.

9. Once the installation gets to the "restart the computer" stage, go ahead and do the
restart, making sure that you select the new Etiona operating system from the GRUB menu. Once
it's opened OK, only then is it time to unplug the flash drive or remove the live DVD.

10. Before invoking sudo apt-get update & sudo apt-get upgrade, be sure to run the following
script:
sudo sed -i s/https/http/ /etc/apt/sources.list

11. Later on, software updater will pop up automatically; go ahead and let it do its thing,
too.

12. Personally, I stick to what's in the Add/Remove Applications repository unless there's
nothing at all there that will do what you must do in the normal course of work.

Thank you very kindly @amenex

This may take some time for me to complete...

Some have weighed in that Flatpak should've had "no relevance" on any such problems as I reported, but since I VERY rarely change anything involving the OS, the fact that the errors appeared exactly when Flatpak was installed, seem far too strong a coincidence too dissuade me entirely.

Your inability to access Trisquel's repository was due to "an outdated Certificate Authority collection", as the first item of https://trisquel.info/en/release-announcement-trisquel-901-etiona-security-update explains.

Software Updater even still lists both Steam and Flatpak as authenticated repositories

We only made you remove their repositories, in /etc/apt/sources.list.d. Still using sudo rm, you can remove the related keys in /etc/apt/trusted.gpg.d. The "Software & Updates" window (I assume you were referring to its "Authentification" tab) should also have a button to do so.

Goal: Since there are still errors after Flatpak's install and subsequent removal,...

What errors?

... I would very much like to go back to a completely unmodified Trisquel, which I think is now 9.0.1, but without removing the HDD (sda), I can't seem to cause any install attempt to access anything but the HDD (the data drive.) The install screens may very well offer some alternative, but I've been unwilling to try it for fear of overwriting the HDD data drive (drive 0 or sda.)

As amenex suggested, you can choose the "Something else" type of installation in Trisquel's installer. It will let you define partitions wherever you want (/ and the swap partition on the SDD for instance). Two things amenex did not suggest but that I would:

1. Backup the users' data before reinstalling Trisquel (you should actually regularly backup those data, for instance using "Back in Time", by default in Trisquel 9);
2. The "Something else" type of installation lets you select the existing partition for /home and choose to *not* format it; that is apparently what you want.

it's apparently not 'safe' to install ANY other things (even when they claim to be entirely 'open source')

You can add PPAs or Guix on Trisquel, install flatpaks, AppImages, etc.