How to run GCC for ARM cross compiling in WSL2 via WINE?

Question

I'm trying to pack my Windows Toolchain into a container image. For that, I use WSL2 and Docker. To run Windows binaries, I use Wine. This works for many Windows tools, but unfortunately, gcc does not work:

# in WSL2, Ubuntu 20.04 LTS
jan@host:/mnt/e/gcc-arm-11.2-2022.02-mingw-w64-i686-arm-none-eabi/bin$ wine arm-none-eabi-gcc.exe -v
wine: Unhandled page fault on execute access to 004B3000 at address 004B3000 (thread 0009), starting debugger...

Debug messages:

Unhandled exception: page fault on execute access to 0x004b3000 in 32-bit code (0x004b3000).
Register dump:
 CS:0023 SS:002b DS:002b ES:002b FS:006b GS:0063
 EIP:004b3000 ESP:012fff24 EBP:012fff48 EFLAGS:00010206(  R- --  I   - -P- )
 EAX:3fff8000 EBX:3ffff000 ECX:012fff74 EDX:012fff74
 ESI:00000000 EDI:00000000
Stack dump:
0x012fff24:  004014f2 00000000 c1aacd00 012fff50
0x012fff34:  7b454882 3ffff000 7b454cfc 7b454cfc
0x012fff44:  7b454cfc 012fffd8 7b454cfc 3ffff000
0x012fff54:  004014e0 012fff74 012fff74 00000000
0x012fff64:  00000000 004014e0 3ffff000 00000000
0x012fff74:  ffffffff 7b46d850 7b434568 00000000
Backtrace:
=>0 0x004b3000 in arm-none-eabi-gcc (+0xb3000) (0x012fff48)
  1 0x7b454cfc in kernel32 (+0x34cfb) (0x012fffd8)
  2 0x7b45488e in kernel32 (+0x3488d) (0x012fffec)
0x004b3000: orb 0x0(%eax),%al
Modules:
Module  Address         Debug info  Name (10 modules)
PE    400000-  6fc000   Dwarf           arm-none-eabi-gcc
PE  7b020000-7b023000   Deferred        kernelbase
PE  7b420000-7b5db000   Export          kernel32
PE  7bc30000-7bc34000   Deferred        ntdll
PE  7f3e0000-7f3e4000   Deferred        imm32
PE  7f610000-7f614000   Deferred        version
PE  7f640000-7f644000   Deferred        advapi32
PE  7f6d0000-7f6d7000   Deferred        gdi32
PE  7f840000-7f928000   Deferred        user32
PE  7fa70000-7fa74000   Deferred        msvcrt
Threads:
process  tid      prio (all id:s are in hex)
00000008 (D) Z:\mnt\e\gcc-arm-11.2-2022.02-mingw-w64-i686-arm-none-eabi\bin\arm-none-eabi-gcc.exe
    00000029    0
    00000009    0 <==
0000000e services.exe
    00000023    0
    0000001c    0
    00000015    0
    00000010    0
    0000000f    0
00000011 plugplay.exe
    00000019    0
    00000018    0
    00000012    0
00000013 explorer.exe
    00000030    0
    0000002f    0
    0000002c    0
    00000014    0
0000001a winedevice.exe
    00000020    0
    0000001f    0
    0000001e    0
    0000001d    0
    0000001b    0
00000021 winedevice.exe
    00000025    0
    00000024    0
    00000022    0
System information:
    Wine build: wine-5.0 (Ubuntu 5.0-3ubuntu1)
    Platform: i386
    Version: Windows 7
    Host system: Linux
    Host version: 5.10.60.1-microsoft-standard-WSL2

GCC is from here: https://developer.arm.com/tools-and-software/open-source-software/developer-tools/gnu-toolchain/downloads-1

Other tools in the directory, like gcov, readelf, etc. don't work either.

Is there anything I can do to track down the issue or is nearly impossible to run a toolchain in Wine?

The reason I have to to use the Windows Version instead the Linux version is that the toolchain is slightly modified by our supplier and Windows only :( But I'd like to avoid to run a Windows Docker Server for one image only, therefore the Wine approach.