NVidia driver installers, regardless of version report the 7-Zip fault. (old downloads that worked in the past or recent downloads)
WinRAR reports no errors with the archives and I can unarchive them successfully manually.

ESET Online scanner can't download and install latest databases, fails every attempt.

Trend-Micro House Call, Windows Defender, and Panda Cloud Cleaner report no infections, neither does MalwareBytes.

Where should I look next?
Is it time to try a clean install of Windows and go through the painful update process?
 
Solution
I would try this first. Run the "Restore health" command.


Afterwards, run SFC Scannow.


If you still have issues after running both utilities, let me know.

It might also be a good idea to uninstall 7zip, restart the system and then install the latest version of 7zip. Do so after running the above utilities.
I would try this first. Run the "Restore health" command.


Afterwards, run SFC Scannow.


If you still have issues after running both utilities, let me know.

It might also be a good idea to uninstall 7zip, restart the system and then install the latest version of 7zip. Do so after running the above utilities.
 
Solution
7-zip has been uninstalled for a few reboots now. I'll definitely look at the DISM and SFC commands and see what that does.

[update:]
Oddly after the last reboot and my running the suggested tools:

SFC said there was something it couldn't fix, yet DISM said there was nothing wrong.
I did get some older NVidia drivers installed for my GPU...
ESET still seems to be having issues with its module update.
 
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Don't run the DISM check, run the DISM /Online /Cleanup-Image /RestoreHealth command. It cannot hurt anything to repair the image even if nothing is wrong with it. After you run the DSIM restorehealth command, and restart the system, THEN run the SFC SCANNOW command. If you did that, it should be ok. There shouldn't be anything SFC SCANNOW can't fix if DISM RESTOREHEALTH has been run.

Of course, nothing every conforms to can't, and is usually more like "shouldn't". Anything can happen when a computer is involved.

What "zip" files are you trying to deal with anyhow?

The Nvidia driver downloads are an .exe, not a .zip or other compressed file like .rar or anything else.