Gorohoroh's solution is close, but instead of selecting "Use braces for multiline" I had to select "Add braces" to force it to add the braces in the single-line scenario. And I had to set that in all six dropdowns under "Force Braces" to catch all the scenarios:
What I was really hoping for was to be able to set up ReSharper to do a yellow warning or red error when the rule was violated, but I haven't found a way to do that. Because you're right, Gorohoroh, Cleanup Code does a lot of stuff and I'd like to have the option to look at and fix the rule violations one at a time.
You should edit your profile for cleaning up. The proper item is called Add/Remove braces for single statements in "if-else", "for", "foreach", "while", "do-while", "using". This item can be found within the C# => Code styles item.
If the item is checked, braces will be added; if unchecked, braces will be removed.
Note: adding doesn't work now (don't know why - perhaps, too fresh version of ReSharper). However, if you will uncheck the mentioned item, the existent braces around single statements will not be removed.
UPD: The problem solved, see the first two comments under this post.
Just if it can help somebody else to save time, on one machine of my company, following Sergey advices was not enough despite the great quality of his post.
On concerned setup (VS2017, R# 2019, both up to date) these settings on R# side were already good, but I also had to modify it in Visual Studio options :
In Options window, go to Text editor -> C# -> Code style ->
Formatting -> General,
Check "Perform Additional code cleanup
during formatting" and "Add/remove braces for single-line control
statement"