此程序将重现您报告的错误：

{$APPTYPE CONSOLE}

uses
  System.SysUtils, System.IOUtils;

var
  FileName: string;

begin
  try
    FileName := TPath.GetTempFileName;
    TFile.WriteAllText(FileName, 'é', TEncoding.ANSI);
    TFile.AppendAllText(FileName, 'é');
  except
    on E: Exception do
      Writeln(E.ClassName, ': ', E.Message);
  end;
end.

在这里，我将原始文件写成ANSI格式。然后调用AppendAllText，它将尝试写成UTF-8格式。发生的事情是，我们最终得到了这个函数：

class procedure TFile.AppendAllText(const Path, Contents: string);
var
  LFileStream: TFileStream;
  LFileEncoding: TEncoding; // encoding of the file
  Buff: TBytes;
  Preamble: TBytes;
  UTFStr: TBytes;
  UTF8Str: TBytes;
begin
  CheckAppendAllTextParameters(Path, nil, False);

  LFileStream := nil;
  try
    try
      LFileStream := DoCreateOpenFile(Path);
      // detect the file encoding
      LFileEncoding := GetEncoding(LFileStream);

      // file is written is ASCII (default ANSI code page)
      if LFileEncoding = TEncoding.ANSI then
      begin
        // Contents can be represented as ASCII;
        // append the contents in ASCII

        UTFStr := TEncoding.ANSI.GetBytes(Contents);
        UTF8Str := TEncoding.UTF8.GetBytes(Contents);

        if TEncoding.UTF8.GetString(UTFStr) = TEncoding.UTF8.GetString(UTF8Str) then
        begin
          LFileStream.Seek(0, TSeekOrigin.soEnd);
          Buff := TEncoding.ANSI.GetBytes(Contents);
        end
        // Contents can be represented only in UTF-8;
        // convert file and Contents encodings to UTF-8
        else
        begin
          // convert file contents to UTF-8
          LFileStream.Seek(0, TSeekOrigin.soBeginning);
          SetLength(Buff, LFileStream.Size);
          LFileStream.ReadBuffer(Buff, Length(Buff));
          Buff := TEncoding.Convert(LFileEncoding, TEncoding.UTF8, Buff);

          // prepare the stream to rewrite the converted file contents
          LFileStream.Size := Length(Buff);
          LFileStream.Seek(0, TSeekOrigin.soBeginning);
          Preamble := TEncoding.UTF8.GetPreamble;
          LFileStream.WriteBuffer(Preamble, Length(Preamble));
          LFileStream.WriteBuffer(Buff, Length(Buff));

          // convert Contents in UTF-8
          Buff := TEncoding.UTF8.GetBytes(Contents);
        end;
      end
      // file is written either in UTF-8 or Unicode (BE or LE);
      // append Contents encoded in UTF-8 to the file
      else
      begin
        LFileStream.Seek(0, TSeekOrigin.soEnd);
        Buff := TEncoding.UTF8.GetBytes(Contents);
      end;

      // write Contents to the stream
      LFileStream.WriteBuffer(Buff, Length(Buff));
    except
      on E: EFileStreamError do
        raise EInOutError.Create(E.Message);
    end;
  finally
    LFileStream.Free;
  end;
end;

错误源于以下行：

if TEncoding.UTF8.GetString(UTFStr) = TEncoding.UTF8.GetString(UTF8Str) then

问题是UTFStr实际上不是有效的UTF-8，因此TEncoding.UTF8.GetString(UTFStr)抛出一个异常。
这是TFile.AppendAllBytes中的一个缺陷。鉴于它完全知道UTFStr是ANSI编码的，它调用TEncoding.UTF8.GetString根本没有意义。
你应该向Embarcadero提交一个bug报告，因为这个缺陷仍然存在于 Delphi 10西雅图中。在此期间，你不应该使用TFile.AppendAllBytes。