What exactly does "Publish language" option?

I have a ClickOnce project - winform app - with two install locations by countries, one for the Czech Republic, one for Slovakia. Whenever I publish for different country I only change the Installation folder and the Publishing folder.

Recently I have localized the app recently to the Slovak language. But in the publish package I have "Publish language" set to Czech for both packages.

According to documentation it should only affect the language of the ClickOnce installer. But in fact it affect the culture of the whole appliaction. I have even added this lines:

    [STAThread]
    static void Main()
    {
        //localization code

        Thread.CurrentThread.CurrentUICulture = new CultureInfo("sk-SK");
        Thread.CurrentThread.CurrentCulture = new CultureInfo("sk-SK");

But after install the app is displayed in the Czech language on Slovak Windows even with this code run at startup. When I change the language to Slovak or Neutral, then it gives the following ClickOnce error on the client (because I have changed the Publish language):

The deployment identity does not match the subscription.

When reinstalled with Slovak "Publish language" it is displayed in Slovak.

Why I do not see Slovak interface even if I set the culture manually within the code and the client has Slovak Windows? Is there a workaround so that I do not have to reinstall all the clients?