Versuch das mal so. StringList statt StringStream und ein explizites Add().
Delphi-Quellcode:
procedure TForm5.btn2Click(Sender: TObject);
var
params: TStringList;
LIndy: TIdHTTP;
LResponse:string;
begin
LIndy:= TIdHTTP.Create();
params := TStringList.Create;
try
params.Add('{"content": "Test"}');
LIndy.Request.ContentType := 'application/json';
LIndy.Request.UserAgent := 'Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/66.0.3359.139 Safari/537.36';
LResponse := LIndy.Post(FUrl, params);
finally
LIndy.Free;
params.Free;
end;
end;