这是我的最终结果，结束了工作thx为您的帮助@ π ντα ε

void cleardown() {
    cout <<"Starting Batch File...\n";
    ofstream batch;
    batch.open("down.bat", ios::out);
    batch << "@echo off\n";
    batch <<"SETLOCAL;\n";
    batch <<"SET \"sourcedir3=C:\\Users\\%username%\\Downloads\"\n";
    batch <<"SET \"keepfile=POOL.bat\"\n";
    batch <<"FOR %%a IN (\"%sourcedir3%\\*\") DO IF /i NOT \"%%~nxa\"==\"%keepfile%\" DEL \"%%a\"\n";
    batch <<"GOTO :EOF\n";
    batch.close();

    system("down.bat  & del down.bat");
    cout <<"Done!" << endl;
    delay();
    system ("cls");
}

发生编译器错误的原因是您没有转义字符串文字中==周围的2个"字符：

batch <<"FOR %%a IN (\"%sourcedir3%\* \") DO IF /i NOT \"%%~nxa"=="%keepfile%\" DEL \"%%a\"\n";
                                                               ^  ^

因此，最后只执行以下部分：

batch <<"FOR %%a IN (\"%sourcedir3%\* \") DO IF /i NOT \"%%~nxa"

其中<<返回一个ostream&对batch的引用，然后尝试使用==运算符将该引用与字符串文本"%keepfile%\" DEL \"%%a\"\n"进行比较。由于ostream没有定义这样的比较，因此编译器出错。
您需要转义这2个"字符，例如：

batch <<"FOR %%a IN (\"%sourcedir3%\* \") DO IF /i NOT \"%%~nxa\"==\"%keepfile%\" DEL \"%%a\"\n";
                                                                ^   ^

还有一个\字符也需要转义：

batch <<"FOR %%a IN (\"%sourcedir3%\* \") DO IF /i NOT \"%%~nxa\"==\"%keepfile%\" DEL \"%%a\"\n";
                                   ^

以及其他字符串常量中的几个\字符：

batch <<"SET \"sourcedir3=C:\Users\%username%\Downloads\"\n" ;
                            ^     ^          ^

也就是说，在C++11和更高版本中，您应该考虑使用raw string literal，这样您就完全不需要担心转义字符，例如：

void cleardown() {
    cout << "Starting Batch File...\n";
    ofstream batch("down.bat");
    batch << "@echo off" << '\n';
    batch << "SETLOCAL;" << '\n';
    batch << R"(SET "sourcedir3=C:\Users\%username%\Downloads")" << '\n';
    batch << R"(SET "keepfile=POOL.bat")" << '\n';
    batch << R"(FOR %%a IN ("%sourcedir3%\*") DO IF /i NOT "%%~nxa"=="%keepfile%" DEL "%%a")" << '\n';
    batch << "GOTO :EOF" << '\n';
    batch.close();

    system("down.bat  & del down.bat");
    cout << "Done!" << endl;
    delay();
    system("cls");
}

或者：

void cleardown() {
    cout << "Starting Batch File...\n";
    ofstream batch("down.bat");
    batch << R"(
@echo off
SETLOCAL;
SET "sourcedir3=C:\Users\%username%\Downloads"
SET "keepfile=POOL.bat"
FOR %%a IN ("%sourcedir3%\*") DO IF /i NOT "%%~nxa"=="%keepfile%" DEL "%%a"
GOTO :EOF
)";
    batch.close();

    system("down.bat  & del down.bat");
    cout << "Done!" << endl;
    delay();
    system("cls");
}

首先，在这种情况下，您根本没有理由写出并执行一个.bat文件，您可以并且应该直接从您自己的代码中删除这些文件（从而满足您的“我只想拥有.exe应用程序”的需求），例如：

#include <iostream>
#include <filesystem>
#include <string>
#include <memory>
#include <stdexcept>

#include <windows.h>
#include <shlobj.h>

using namespace std;
namespace fs = std::filesystem;

fs::path GetDownloadsPath() {
    // Ask the OS where the folder is actually located, do not hard-code it!
    // It is NOT located at C:\Users\%username%\Downloads on everyone's machine,
    // but the OS always knows where it actually is...
    PWSTR pszPath = nullptr;
    if (FAILED(SHGetKnownFolderPath(FOLDERID_Downloads, 0, nullptr, &pszPath)))
        throw std::runtime_error("Can't get path to Downloads folder");
    std::unique_ptr<WCHAR, decltype(&CoTaskMemFree)> deleter(pszPath, &CoTaskMemFree);
    return fs::path(pszPath);
}

int CompareInsensitive(const wstring &str1, const wstring &str2) {
    return CompareStringW(LOCALE_INVARIANT, NORM_IGNORECASE, str1.c_str(), str1.size(), str2.c_str(), str2.size()) - 2;
    // alternatively:
    // return CompareStringOrdinal(str1.c_str(), str1.size(), str2.c_str(), str2.size(), TRUE) - 2;
}

void cleardown() {
    cout << "Deleting Files...\n";

    const fs::path sourcedir = GetDownloadsPath();
    const wstring keepfile = L"POOL.bat";

    for (const auto &dir_entry : fs::directory_iterator(sourcedir))
    {
        const fs::path dir_path = dir_entry.path();
        if (CompareInsensitive(dir_path.filename(), keepfile) != 0) {
            fs::remove(dir_path);
        }
    }

    cout << "Done!" << endl;
    delay();
    system("cls");
}