Is mixing modules and headers in C++20 possible / acceptable?

Question

I'm actually trying to understand the C++20 modules system by writing my own little module. Let's say I want to provide a function that deletes all the spaces at the beginning and the end of a string (a trim function). The following code works without problem.

module;

export module String;

import std.core;

export std::string delete_all_spaces(std::string const & string)
{
    std::string copy { string };

    auto first_non_space { std::find_if_not(std::begin(copy), std::end(copy), isspace) };
    copy.erase(std::begin(copy), first_non_space);

    std::reverse(std::begin(copy), std::end(copy));
    first_non_space = std::find_if_not(std::begin(copy), std::end(copy), isspace);
    copy.erase(std::begin(copy), first_non_space);
    std::reverse(std::begin(copy), std::end(copy));

    return copy;
}

import std.core;
import String;

int main()
{
    std::cout << delete_all_spaces("  Hello World!    \n");
    return 0;
}

But what if I want to use only specific headers instead of std.core in my module? If I do so, replacing the import std.core by the following code, I get an error on Visual Studio 2019.

module;

#include <algorithm>
#include <cctype>
#include <string>

export module String;

// No more import of std.core

export std::string delete_all_spaces(std::string const & string)
{
    // ...
}

Error LNK1179 file not valid or damaged: '??$_Deallocate@$07$0A@@std@@YAXPAXI@Z' COMDAT duplicated

However, if in the main.cpp I remplace as well the import std.core with #include <iostream>, the code compiles again. It's like using both system provents the linker to do its job.

The question is: am I doing it wrong? Is it a bad practice to use both the new import and the old #include methods? I saw on multiple posts on the Internet that you can include some old headers in your module, thus modernizing your code without breaking the existing. But what if this header includes some part of the STL, like #include <string> but my module uses import std.core?

I'm testing only with Visual Studio 2019 because, as of now, import std.core does not work with GCC. So, may it comes from a bug in VS? Or will the problem be the same for all compilers?