Introduction
The code in this section is not the answer!
Having unsuccessfully tried to find an answer to my question (I was probably looking badly), I decided to do what I should have done from the very beginning - look in the help node-module less. Having executed the command, I received an exhaustive answer -
-x, --compress Compresses output by removing some whitespaces.
Here it is! - I thought, added the --compress flag in the File Watcher settings and got ... minimized warning file
The compress option has been deprecated. We recommend you use a dedicated css minifier, for instance see less-plugin-clean-css.html
Then I proceeded to the page https://github.com/less/less-plugin-clean-css , where I found the final, working instruction.
Work Answer
You need to additionally install the module less-plugin-clean-css with the command
npm install -g less-plugin-clean-css
and then add to Watcher's arguments
--clean-css="--s1 --advanced --compatibility=ie8"
in the end, the Watcher settings in my case looked like this:

The file is minimized, but with saved comments. A description of all the arguments to the clean-css module can be found at https://github.com/jakubpawlowicz/clean-css . There I found the answer, how to minimize comments when minimizing :
it is required to add the --s0 flag to the arguments for --clean-css (in my case, correct the existing --s1 flag) in this way:
--clean-css="--s0 --advanced --compatibility=ie8"