Pushed to GnuPG master. Let us test. For my machine of Debian GNU/Linux, Wine emulation (Windows 32-bit, Windows 64-bit), make check goes all well.
After confirming the implementation, I'd like to put it into gpgrt.

I learned that Unix build environment needs Wine emulation (with winepath) for MinGW host (when uninstalled executable should run correctly).
https://www.gnu.org/software/libtool/manual/html_node/File-name-conversion.html

Fixed in 1.47.

Fixed in libgcrypt 1.10.2.

Fixed in libgpg-error 1.47.

Fixed in 1.10.2.

In T6388#168750, @gniibe wrote:

Thank you for the bug report.

I see your problem. We need to improve the patch, as we cannot use Bash-only feature in configure.
[...]
That is, prefer possible_libdir1 when not used. Please test this.

I'll add new error codes to gpgrt

Any volunteers to write a manual? ;-)

The reason may be the following text/comment I found in gpgrt.texi:

This manual documents the Libgpg-error library application programming
interface (API). The goal is to that all functions and data types
provided by the library are explained. However, for now this is only
a stub and not very useful.

@tlaurion Thank you for the report, but your particular problem is irrelevant to this ticket.
I lightly looked the log and noticed that the cross build would have some confusions for pkg-config, however, that's not our problem but yours.
For the particular failures in your build, the issues look like a problem of musl linker. It seems that it requires all dependency of libraries to be used, even if an executable doesn't use a library directly.
If it is the case, we need a patch... something like:

@gniibe
Trying to crosscompile newer 2.4 gpg toolstack from Heads OSF under PR https://github.com/osresearch/heads/pull/1350

FWIW, some cards don't have PUKs but two PINs which are able to unblock reciprocal.

Should we also differentiate between wrong PUK and no PUK set?

Having GPG_ERR_BAD_PUK makes sense. So, I added a tag for gpg-error.

Fixed in master (of libgpg-error).
Pushed the change to libgcrypt (master and 1.10 branch).

Ah, I had not done git pull for a week, and I didn't realize your patch.

I pushed a similar fix last week: rE885a287a57cf060b4c
and gnupg has a hack to fix it for oler libgpg-error versions.

Something like this should fix the behavior:

diff --git a/src/argparse.c b/src/argparse.c
index ef0c161..403c4a7 100644
--- a/src/argparse.c
+++ b/src/argparse.c
@@ -3000,7 +3000,13 @@ show_help (opttable_t *opts, unsigned int nopts, unsigned int flags)
         writestrings (0, "Options:", "\n", NULL);
       for (i=0; i < nopts; i++ )
         {
-          s = map_fixed_string (_( opts[ordtbl[i]].description ));
+          if ((opts[ordtbl[i]].flags & ARGPARSE_OPT_HEADER)
+              && opts[ordtbl[i]].description
+              && !*opts[ordtbl[i]].description)
+            /* It's empty header.  */
+            s = opts[ordtbl[i]].description;
+          else
+            s = map_fixed_string (_( opts[ordtbl[i]].description ));
           if ( s && *s== '@' && !s[1] ) /* Hide this line.  */
             continue;
           if ( s && (opts[ordtbl[i]].flags & ARGPARSE_OPT_HEADER))

AFAIU, gpgrt-config works well now for the multilib MinGW target.

Thanks !

A real fix will be in the next gpgrt release

On Windows, closing/inheriting handles is different to POSIX.
https://devblogs.microsoft.com/oldnewthing/20111216-00/?p=8873
https://devblogs.microsoft.com/oldnewthing/20130426-00/?p=4543
https://learn.microsoft.com/en-us/windows/win32/api/processthreadsapi/nf-processthreadsapi-createprocessw
https://learn.microsoft.com/en-us/windows/win32/api/winbase/ns-winbase-startupinfoexw
https://learn.microsoft.com/en-us/windows/win32/api/processthreadsapi/nf-processthreadsapi-initializeprocthreadattributelist
https://learn.microsoft.com/en-us/windows/win32/api/processthreadsapi/nf-processthreadsapi-updateprocthreadattribute
https://learn.microsoft.com/en-us/windows/win32/api/processthreadsapi/nf-processthreadsapi-deleteprocthreadattributelist

We should consider to break the Assuan API maybe we can do that without too many problems for the current use cases.

I'm going to use gnupg_process_* prefix for the functions.

Last two points are for future changes of assuan internal; For the case of controlling fds in detail, it is possible to use spawn callback controlling fds by the routine and let no-touching (inherit) by the spawn function.

I don't understand the last two points: This is only about the three standard descriptors but how shall we supply more descriptors? At least in GPGME we definitely need more.

Evaluating again, I'd like to change spawn functions like this one in libgpg-error:

Examining again, I realized that the current spawn API (not published yet, only available in libgpg-error master) is not that useful in general (or difficult to use), while it works somehow.

Here is the change of GnuPG to use new spawn functions from libgpg-error:

For the spawn_cb, I reconsider. Having three calls complicates use, and it is actually not needed. In the case of pthread_atfork, it is needed, because fork may be used deeply in some functions. In our use cases of spawn function, prepare part of the callback can be called before calling spawn, and parent part of the callback can be called after calling spawn.

I decide use of pid_t, as there are different semantics between POSIX and Windows, *and* there is a problem of MinGW-w64. I introduce gpgrt_process_t, instead.

Another thing when we define a type which represents process.
For pid_t, MinGW-w64 has a bug: https://bugzilla.redhat.com/show_bug.cgi?id=1397787 (or https://sourceforge.net/p/mingw-w64/mailman/mingw-w64-public/thread/1456671365-21759-1-git-send-email-sw%40weilnetz.de/).
(1) GetCurrentProcessId always returns 32-bit (DWORD), so, it can be represented in 32-bit (although DWORD is unsigned).
(2) POSIX requires pid_t should be signed integer https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/sys_types.h.html
(3) Original MinGW defines pid_t as int (in include/sys/type.h by _pid_t). (checked in mingwrt-5.4.2)