When you know what you do - then the code is better

refactored.js

[HttpPost]
public HttpResponseMessage UpdateElementIdManual(Parameters parameters)
{
  _logger.Debug("some useful info here");

  try
  {
    var eletran = ctx.ElementTransactions.Where(s => s.ElementNo == parameters.ElementId).First();
    var dt = DateTime.Parse(eletran.DocumentPeriod + "-01");
    var documentPeriod = string.IsNullOrWhiteSpace(eletran.DocumentPeriodType) ? $"{dt:MMM}-{dt:yy}" : $"{dt:MMM}-{dt:yy} {eletran.DocumentPeriodType}";

    var inv = ctx.Elements.Where(s => s.ElementNo == parameters.ElementId).ToList();
    var minTableName = ctx.TableName.Where(s => s.ElementId == parameters.ElementId).First();
    
    // helper variable to decipher logic 
    var invCountIsZero = inv.Count == 0;    
    var sameEntity = minTableName.Entity == eletran.Customer;
    var sameMonth = minTableName.Month == documentPeriod;    
    
    if (invCountIsZero == 0 && sameEntity && sameMonth)
    {
      eletran.TranStatus = "Manually Generated";
      eletran.ElementNo = parameters.ElementId;
      ctx.SaveChanges();
      // what we shall return here is....just response
      // that means when there is ok and text, then we have an issue
      // so returning ok + text means an error and the schema is broken ... wtf
      return new HttpResponseMessage();
    }

    return new HttpResponseMessage
    {
      Content = new StringContent($"REDACTED1 Same month:{sameMonth}, Same entity: {sameEntity}"),
      StatusCode = System.Net.HttpStatusCode.BadRequest,      
    };

// we shall catch null 
  catch (InvalidOperationException noData)
  {
    _logger.Error(noData);
    return new HttpResponseMessage
    {
      StatusCode = HttpStatusCode.NotFound,
    };
  }
  catch (Exception ex)
  {
    _logger.Error(ex);
    return new HttpResponseMessage
    {
      StatusCode = HttpStatusCode.InternalServerError,      
    };    
  }
}