Putting formatted text to a file and then opening it in a RichEdit

I have a Delphi Form program, where I enter data with different accounts, and do stuff like create a new account, a new client, a new flight, and so on.

I've created a log file where different things get added to it. I want to be able to change the color of the different messages. For example: New Login: Admin (should be green); Admin logged out (should be red).

I try to do it by entering the text to a TRichEdit variable, then I try to set the color and I give it to a TMemo variable, so I can then give the text with tags to a WordPad file (RTF). After that, I try to load the file, but unsuccessfully.

I tried loading it directly to a TRichEdit, which results in getting the text with tags instead of it being formatted.

I've also tried giving it to a TMemo first then to the RichEdit, but I get an empty text.

This is the code I use to give the text from the TRichEdit to the TMemo in order to have the tags in the file later:

procedure GetLogFormatting(richEditLog : TRichEdit; textColor : TColor);
var
  sStream : TStringStream;
begin
  with frmMain do
  begin
    logText.Clear;
    memLog.Clear;
    sStream := TStringStream.Create;
    richEditLog.Lines.SaveToStream(sStream);
    richEditLog.SelAttributes.Color := textColor;
    memLog.Lines.Add(sStream.DataString);
    FreeAndNil(sStream);
  end;
end;

This is the code I use to make the log line and then give it to the TMemo with the procedure above:

dateTimeNow := Now;

logText.Lines.Add('<' + DateTimeToStr(dateTimeNow) + '> A client was deleted');
GetLogFormatting(logText, clRed);

This is how I give the log lines to the file (I call the procedure whenever there is a change in accounts, or when the program is closed):

procedure AddToLogFile();
var
  i : integer;
  s : string;
begin
  with frmMain do
  begin
    AssignFile(logFile, 'C:\LogFileColor.rtf');
    Append(logFile);
    for i := 0 to memLog.Lines.Count do
    begin
      s := memLog.Lines.Text;
      Writeln(logFile, memLog.Lines[i]);
    end;
    CloseFile(logFile);
  end;
end;

This is how I give the text from the file to the TRichEdit in the form:

procedure OpenLogForm(dateFilter : Boolean; searchDate : tDate);
var
  sLine, sTime : string;
  dateExists : Boolean;
  newMemo : TMemo;
  sStream : TStringStream;
begin
  with frmMain do
  begin    
    newMemo := TMemo.Create(frmLogSearch);
    newMemo.Parent := frmLogSearch;
    newMemo.Width := frmLogSearch.tLogRichEdit.Width;
    newMemo.Visible := False;

    sStream := TStringStream.Create;

    dateExists := false;
    frmLogSearch.tLogRichEdit.Clear;
    
    AssignFile(logFile, 'C:\LogFileColor.rtf');
    Reset(logFile);

    while not Eof(logFile) do
    begin
      newMemo.Clear;
      
      Readln(logFile, sLine);
      
      if dateFilter then
      begin
        sTime := DateTimeToStr(searchDate);   

        if (Pos(sTime, sLine) <> 0)then
        begin
          newMemo.Lines.Add(sLine);
          sStream.WriteString(newMemo.Lines.Text);
          frmLogSearch.tLogRichEdit.Lines.LoadFromStream(sStream);
          dateExists := true;
        end;
      end
      else
      begin
        newMemo.Lines.Add(sLine);
        sStream.WriteString(newMemo.Lines.Text);
        frmLogSearch.tLogRichEdit.Lines.LoadFromStream(sStream);
        dateExists := True;
      end;
    end;

    if dateExists = false then
    begin
      ShowMessage('There is no such text from that date! Try another text');
    end;

    CloseFile(logFile);
    newMemo.Destroy;
  end;
end;

Can someone help me understand what I'm doing wrong, and how to fix it? I can't seem to find a lot on the Internet.