Block the connections via the hosts file.
https://gtm.steamproxy.vip/groups/penguindome/discussions/19/4297068274224693303/

Important for blocking: remove the hash symbol in front of each entry. The UGC is the cloud server for uploading user-generated content. Not everyone may want to disable that.

Raining steam clouds?

huh

Me personally? No.

I believe this is a bug in Steam, because I've read about this many times, for many years.
If the Steam Cloud becomes enabled for whatever reason, and if you don't want that, then you can manually turn the Cloud off again. You can read about how to turn it off here:
https://help.steampowered.com/en/faqs/view/68D2-35AB-09A9-7678

There is also a bug report forum in this Steam group:
https://gtm.steamproxy.vip/groups/SteamClientBeta
But it's for the Beta application. However, you might run that on your computer as well, to test if the bug persists in the Beta version. If so, you can report it.

I would, but Steam doesn't let me get my hands on their code.

No, the original post was a copy of the support request.

After checking, I found that Steam cloud turns on when Steam starts in "online" mode, so I stay in "offline" mode 'till needed.

Response from support on this issue:

"Hello,

I am sorry that you are having an issue with the Steam Cloud.

Steam Support has a limited ability to resolve these issues as Steam Cloud is an automated system. If you have disabled it once for the game it should remain disabled.

I would encourage you to read our Steam Cloud FAQ. Although it may seem like a long article, it can resolve a number of common issues, while helping you understand how the cloud works. The cloud troubleshooting section can also help to ensure that your machine is in a good state for the cloud to function correctly.

Additionally, if you have any antivirus program running please make sure to add Steam as an exception to it or temporarily disable/uninstall it and also check for
interfering programs running and stop running them.

If you continue to see the issue after stopping any interfering programs, you'll want to download the Steam installer again in order to repair your local Steam installation. Once you have the installer, run it and select the current file path of your Steam installation. This will make sure that you have all of the correct files in the correct locations, while preserving installed games and other account specific details.

Steam Support
Ksenia"

Message from you on Jun 4 @ 2:46am | 3 minutes ago

For future reference, if I start STEAM in "online" mode, it turns on the "STEAM-SETTINGS-CLOUD-ENABLE STEAM CLOUD" switch, with or without an internet connection, but it does not happen when starting in "offline" mode.
It seems a number of people have mentioned this issue.