malone wrote:

.... well, it's a mystery to me. Perhaps someone can explain it?

I shut down my Windows 10 computer at the end of every day. There are
two ways I have for doing this. First, I can go to the start button and
select "power" then "shut down". The other way, which is what I usually
do, is simply to press the power button. (I've configured my system
settings so that when I press the power button the computer shuts down.)

I have assumed that both these methods do the same thing. Shut down the
computer. But there's a subtle difference when I restart the computer.
If I have previously shut down simply by pressing the power button
everything boots up normally. However, if I have previously shut down
via the start button, everything boots up fine - except for the addition
of the rather tiresome splash screen exhorting me to install Microsoft
Office. This never appears when I boot after shutting down by pressing
the power button.

I know that with a bit of effort I could probably find out how to
prevent that screen from appearing, but that's not my point. Especially
as I shut down via the start button only infrequently. The issue for me
is what is the difference between the different methods of shutting down
my computer?

You could use SysInternals' Process Explorer to see what process has a
window handle on that prompt for Office. When the prompt appears, load
Process Explorer. Use its spider web toolbar icon to drag onto the
prompt window. Process Explorer will highlight which process owns that
window. Once you know the executable filename, you might be able to
search on it to find out where it is.

No idea if this is a new problem with an old computer or a new problem
with a new computer. If the latter, did you build the computer or did
you buy a pre-built? If a pre-built, those often comes with LOTS of
bundleware, including trial versions of anti-virus and, yep, Office.
Even if a trial version, it should be listed the Add/Remove Programs
applet.