public void ChangeVersion( 
   VersionBase fromVersionBase,
   VersionBase toVersionBase
)

{
  // Must be called within QueuedTask.Run
  void ChangeVersions(Geodatabase geodatabase, string toVersionName)
  {
    using (VersionManager versionManager = geodatabase.GetVersionManager())
    {
      VersionBaseType versionBaseType = versionManager.GetCurrentVersionBaseType();

      if (versionBaseType == VersionBaseType.Version)
      {
        Version fromVersion = versionManager.GetCurrentVersion();
        Version toVersion = versionManager.GetVersion(toVersionName);

        // Switch between versions
        MapView.Active.Map.ChangeVersion(fromVersion, toVersion);
      }

      if (versionBaseType == VersionBaseType.HistoricalVersion)
      {
        HistoricalVersion fromHistoricalVersion = versionManager.GetCurrentHistoricalVersion();
        HistoricalVersion toHistoricalVersion = versionManager.GetHistoricalVersion(toVersionName);

        // Switch between historical versions
        MapView.Active.Map.ChangeVersion(fromHistoricalVersion, toHistoricalVersion);
      }

      // Switch from HistoricalVersion to Version and vice-versa 
      // MapView.Active.Map.ChangeVersion(fromHistoricalVersion, toVersion);
      // MapView.Active.Map.ChangeVersion(fromVersion, toHistoricalVersion);
    }
  }
}

{
    //Note: needs to be called on the MCT
    //Getting the current version name from the first feature layer of the map
    Datastore dataStore = featureLayer.GetFeatureClass().GetDatastore();  //getting datasource
    Geodatabase geodatabase = dataStore as Geodatabase; //casting to Geodatabase
    if (geodatabase == null)
        return;

    VersionManager versionManager = geodatabase.GetVersionManager();
    ArcGIS.Core.Data.Version currentVersion = versionManager.GetCurrentVersion();
    string currentVersionName = currentVersion.GetName();

    //Getting all available versions except the current one
    List<ArcGIS.Core.Data.Version> versions = [];
    foreach (string versionName in versionManager.GetVersionNames())
    {
        if (versionName != currentVersionName)
            break;
        versions.Add(versionManager.GetVersion(versionName));
    }

    //Assuming there is at least one other version we pick the first one from the list
    ArcGIS.Core.Data.Version toVersion = versions.FirstOrDefault();
    if (toVersion != null)
    {
        //Changing version
        MapView.Active.Map.ChangeVersion(currentVersion, toVersion);
    }
}