The problem may be your antivirus or firewall setting.

Thank you, David. I disabled my AV. Still fails.

Just to clarify-- Thunderbird is working satisfactorily, but checks for updates fail. Is a VPN being used? I have never seen this problem, and I'm clueless on fixing it. An option would be to download from https://www.thunderbird.net/en-US/thunderbird/all/ and install over the top of the current version. I always recommend doing backups prior to updates.

Exactly the problem, and I have been downloading and applying the updates "manually." Thanks for thinking about it.

You're welcome. I'm glad it works.

Of course I'd prefer if the update function worked as intended. Anyone have any idea which Internet security protocol(s) on which the TBird/Supernova Update function relies?

Check Settings > Show update history.

Update History shows recent successes from manual downloads/installs. Clicking on "Check for updates" produces a "Failed to check for update" error. Clicking on "Release notes" produces a "We're having trouble finding that site" error that further says, "Thunderbird.Net could not be found." Clicking on "Details" produces a "Can't connect to the server" error message. This occurs only from inside TBird. I can connect to both Thunderbird.Net and the "Details" URL (https://www.thunderbird.net/en-US/thunderbird/115.6.0/releasenotes/?uri=/thunderbird/releasenotes/&locale=en-US&version=115.6.0&channel=release) from outside TBird.

Is your computer managed by your employer, school, or another organization?

Check the update debug log and other update files:

1. Open config editor https://support.mozilla.org/en-US/kb/config-editor
2. Set app.update.log to true.
3. Open the Browser Console either with the hotkey Control+Shift+J (Command+Shift+J on macOS), or via Hamburger Menu->More Tools->Browser Console
4. In the Filter textbox at the top, enter AUS: to filter out everything except the update messages. Check that Logs is highlighted at "Errors Warnings Logs".
5. In Settings, type or paste "updates" and click on the button "Update to xxx".
6. Once the update check has completed, copy the messages out of the Browser Console and attach them here.
7. Navigate to Help > Troubleshooting Information
8. Find the "Update Folder" entry and click "Open Folder" or "Show in Finder"
9. Locate the file updates.xml and attach them here.
10. Open the updates directory.
11. Inside, you should find files named last-update.log and backup-update.log. Attach both files here.

Thank you for taking time to help me with this, Wayne. It's much appreciated, particularly during this season when I'm sure you have other things you'd rather be doing.

These are not managed computers.

My wife is waiting in the car even as I type. When I join her, I will get "the look," but I wanted to respond. I will step through the instructions and gather the logs after tomorrow.

Happy holidays!

Solved it. I changed my router's DNS settings in DHCP, which I'd set manually, back to automatic, and the problem disappeared. It showed up only on the laptops because their wireless connections uses DHCP where everything else on the network used static IPs. Thanks for taking time to try to help.

I would suggest you enable the setting for DNS over HTTPS in Thunderbird settings. This uses cloudflare for DNS and because of the encrypted nature of the connection stops your ISP from snooping on what sites you lookup (even if you do not visit them).

It has the added benefit of using a DNS service that is not controlled by your ISP. This is most noticeably for those with providers like ATT and some others that use DNS poisoning to reroute requests for their own benefit.

The final benefit is you will never have issues from messed up DNS settings in network protocols going forward.

Done. Thanks very much.