Previous keyboard shortcut to switch off Orca after system startup (Super + Alt + SS) no longer works

>text-to-speech accessibility tool
In the accessibility menu, it's called "screen reader with speech".

I have half solved the problem.
man orca led me to orca -s which brings up a GUI for setting preferences for Orca, which has an option to deactivate speech, and that works across sessions. (I was at first not able to directly edit Orca's config file because there was no config file before my usage of the GUI caused one to be created.)

So, the progress is that I no longer need to stop Orca from speaking when I start a session, and Orca no longer weighs down on the system.

But Orca still needlessly autostarts at the beginning of every session (but stays silent).

Update:
Turns out there is a reason for me to not have Orca running at all, rather than just telling it not to speak:
As long as Orca is running, even while in no-speak-mode, Abrowser is in what feels very much like caret browsing mode, except that, unlike Abrowser's real caret browsing mode, the caret position is not visible. I guess this is a feature rather than a bug, and something I did caused this behaviour.
It took me a while to figure out Orca was involved and using the system monitor to manually forcibly end Orca returned Abrowser behaviour to normal, non-caret browsing, whereas pressing Abrowser's shortcut for caret browsing did NOT help; it only toggled between Orca caret browsing mode (without visible caret) and Abrowser's own built-in caret browsing mode (with visible caret).

As a side note, I had trouble navigating the current (as of 2024) Trisquel forum webpages in caret browsing mode:
In a thread of several posts, it seemed impossible to use caret browsing to go all the way down or all the way back up; as long as I only used the ↓ and ↑ keys, the caret always seemed to get stuck inside only one part of the page. Instead, I had to rely on other ways such as pressing the space bar to get down, or using either the mouse wheel or mouse-dragging the scrolling bar to get down or up. I hope the future Trisquel website will not let the caret get stuck anywhere.

So, how do I once and for all prevent Orca (and while I'm at it, Trisquel's bluetooth manager, as I don't even own any bluetooth devices) from autostarting each session?

At the location ~/.config/autostart/ create a file orca.desktop with contents [Desktop Entry]
Hidden=true. File must end with an empty line. Reboot.
Similar file can be created for "bluetooth manager", you have to name is as the name of the service with .desktop extension attached.

Create/edit the autostart directory and .desktop files as necessary.

Hope this helps.

You may also need to install and launch dconf-editor. Go to org → gnome → desktop → a11y → applications, turn off screen-reader-enabled.

Hope this helps.

Just for the reference, my orca.desktop file looks like this
[Desktop Entry]
Type=Application
Name=Orca screen reader
Exec=orca
NoDisplay=true
AutostartCondition=GSettings org.gnome.desktop.a11y.applications screen-reader-enabled
X-GNOME-AutoRestart=true
#X-GNOME-Autostart-Phase=Initialization
OnlyShowIn=GNOME;MATE;Unity;Cinnamon;
It only autostarts if screen-reader-enabled is turned on.

TL;DR: Solved. Probably by following emekarmead's advice, but bizarrely not by following prospero's advice. Thanks to both of you for your suggestions.

Yes, I am running MATE as desktop environment, according to neofetch output.

I opened
Main Menu > System > Preferences > Personal > Startup applications
(I am ashamed to say I had somehow overlooked that menu item, even though it has been in the Main Menu and the Control Center all this time), checked "Show hidden", and unchecked "Orca screen reader / No description". I also unchecked "Blueman Applet". After that, Blueman no longer autostarted each session. But Orca still did.

I also ran "dconf Editor", where there are Orca-related settings at three or more places:

• > org > mate > desktop > applications > at > screen-reader-enabled
  "Whether the screen reader is turned on."
• > org > gnome > desktop > a11y > applications > screen-reader-enabled
  "Whether the screen reader is turned on."
• > com > canonical > unity-greeter > screen-reader
  "Whether to enable the screen reader".

I changed all three to a current value of "false". But Orca still autostarted each session.

After that,
/etc/xdg/autostart/orca-autostart.desktop
consisted of
[Desktop Entry]
Type=Application
Name=Orca screen reader
Exec=orca
NoDisplay=true
AutostartCondition=GSettings org.gnome.desktop.a11y.applications screen-reader-enabled
X-GNOME-AutoRestart=true
#X-GNOME-Autostart-Phase=Initialization
OnlyShowIn=GNOME;MATE;Unity;Cinnamon;
X-Ubuntu-Gettext-Domain=AC_PACKAGE_TARNAME
with no empty last line, whatever that means. Next, I wondered what the X-GNOME-AutoRestart value does, so I manually changed it to "false". Didn't help.

I still used the System Monitor to manually "end" Orca's process first thing after logging in each session. That worked most of the times. But sometimes, it would not, Orca would not end, and the System Monitor would show an unusually high CPU load. In those cases, I instructed the System Monitor to "kill" Orca; that always worked, Orca would disappear from the list of processes, and the high CPU load would die down, back to normal.

Orca still autostarted at each new session, which was a minor inconvenience, so I gave up, I submitted to the helpful toothed whale. One more reason to switch from Trisquel (with MATE) back to Trisquel Mini next time, which I found less irritating to use and which I hope Trisquel won't drop anytime soon.

But then I remembered and re-read emekarmead's suggestion, I created ~/.config/autostart/orca.desktop (the autostart folder already contained other files, among which one named orca-autostart.desktop, without empty last line) with contents
[Desktop Entry]
Hidden=true
and an empty line, and logged out and back in (instead of emekarmead's suggested full reboot; I should read more carefully), and Orca still autostarted. Then I further edited both
~/.config/autostart/orca.desktop
and
~/.config/autostart/orca-autostart.desktop
making sure both of them contain, among their other lines,
Hidden=true
X-MATE-Autostart-enabled=false
, whatever those mean. And I don't know whether that is what fixed it, or the following reboot instead of just logging out and back in, but since that reboot, System Manager has not shown an Orca process. Great success.

I am a bit disappointed that neither unchecking Orca in the "Startup applications" menu nor using dconf editor automatically created an accordingly filled ~/.config/autostart/orca.desktop (or accordingly edited ~/.config/autostart/orca-autostart.desktop, if that would have done the job) and that I had to do this manually, when the Blueman issue was so straightforward to solve.

I think my system has had one or two hiccups that caused some settings to get lost; I think one was long ago but I can't remember, and one was perhaps caused by that recent update which seems to have broken the keyboard shortcut to toggle Orca as mentioned in OP.