After several hours of fighting, I think I came up with really simple and universal solution. None of solutions I found were working for me ('Publish' target is for ClickOnce only), so I came up with this:
Publish file (pubxml) is just project-like file. So add some value, for example:
<IsPublish>True</IsPublish>
and then in project file:
<Target Name="MessageBeforePublish" AfterTargets="Build" Condition="'$(IsPublish)' == 'True'">
    <Message Text="Before publishing..." Importance="high" />
  </Target>
So, to be clear, my pubxml file looks like that:
<?xml version="1.0" encoding="utf-8"?>
<!--
https://go.microsoft.com/fwlink/?LinkID=208121. 
-->
<Project ToolsVersion="4.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
  <PropertyGroup>
    <Configuration>Release</Configuration>
    <Platform>x64</Platform>
    <PublishDir>***my dir***</PublishDir>
    <PublishProtocol>FileSystem</PublishProtocol>
    <TargetFramework>netcoreapp3.1</TargetFramework>
    <RuntimeIdentifier>win-x64</RuntimeIdentifier>
    <SelfContained>true</SelfContained>
    <PublishSingleFile>False</PublishSingleFile>
    <PublishReadyToRun>True</PublishReadyToRun>
    <PublishTrimmed>False</PublishTrimmed>
    <IsPublish>True</IsPublish>
  </PropertyGroup>
</Project>
Notice the last property (IsPublish) added by me.
That's it.