static void

Changing AppSettings in tests

ConfigurationManager.AppSettings is a static dependency, so how can you unit test? Actually it's pretty easy - GetSection, Save, RefreshSection.
The only caveat is you must have an app.config in your test project, even if it's empty.

[TestClass]
public class ChangeConfigurationTest
{
    private const string Value = "Hello";
    private const string KeyValue = "MySetting";
 
    private static void ChangeConfiguration()
    {
        //the .config must exist (AppSettings doesn't have to be there).
        //if your test class doesn't have an App.config, this succeeds but the new appSetting is not loaded.
        var config = ConfigurationManager.OpenExeConfiguration(Assembly.GetCallingAssembly().Location);
        var appSettings = (AppSettingsSection)config.GetSection("appSettings");
        appSettings.Settings.Clear();
        appSettings.Settings.Add(KeyValue, Value);
        config.Save();
        ConfigurationManager.RefreshSection("appSettings");
    }
 
    [TestMethod]
    public void TestMethod1()
    {
        var setting = ConfigurationManager.AppSettings[KeyValue];
        Assert.AreEqual(true, string.IsNullOrEmpty(setting));
        ChangeConfiguration();
        setting = ConfigurationManager.AppSettings[KeyValue];
        Assert.AreEqual(Value, setting);
    }
}

ConnectionStrings

The corresponding code for a connection string.

private static void ChangeConfiguration()
{
    var config = ConfigurationManager.OpenExeConfiguration(Assembly.GetCallingAssembly().Location);
    var connectionStrings = (ConnectionStringsSection)config.GetSection("connectionStrings");
    connectionStrings.ConnectionStrings["MyDatabase"]
        .ConnectionString = @"Data Source=C:\Dev\commands.sqlite";
    config.Save();
    ConfigurationManager.RefreshSection("connectionStrings");
}