There appears to be a stale session blocking the port.
Could you please try running:

kex --kill && sudo kex --kill

to kill all remnants from earlier sessions and then try again?

I've tried this command, but it still has the same problem

┌──(shine㉿Shadow)-[~]
└─$ kex --kill && sudo kex --kill

┌──(shine㉿Shadow)-[~]
└─$ kex --win -s 1 ⨯

Error connecting to the KeX server.
Please try "kex start" to start the service.
If the server fails to start, please try "kex kill" or restart your WSL2 session and try again.

Could you please run "kex --status" and "kex --win --status" and post the output?

Many thanks

This is the case when an normal user runs two commands：
┌──(shine㉿Shadow)-[~]
└─$ kex --status

    Kex Server is stopped.
    Win-KeX SL is stopped.
    Win-KeX ESM is stopped.
    '/tmp/.X11-unix' is a Win-KeX socket

┌──(shine㉿Shadow)-[~]
└─$ kex --win --status

Error connecting to the KeX server.
Please try "kex start" to start the service.
If the server fails to start, please try "kex kill" or restart your WSL2 session and try again.

This is the case when I run two commands after using sudo：
┌──(shine㉿Shadow)-[~]
└─$ sudo kex --status

    KeX Server is running.

/usr/bin/kex:行266: tasklist.exe：未找到命令
Win-KeX SL is stopped.
Win-KeX ESM is stopped.
'/tmp/.X11-unix' is a Win-KeX socket

┌──(shine㉿Shadow)-[~]
└─$ sudo kex --win --status

Win-KeX server sessions:

X DISPLAY # RFB PORT # RFB UNIX PATH PROCESS ID # SERVER
1 5901 7960 (stale) Xtigervnc

You can use the Win-KeX client to connect to any of these displays.

I wonder if it's because the Win-Kex socket doesn't have permission to my normal user：

This is the file owner I found in the folder where the Win-Kex socket is located：
┌──(shine㉿Shadow)-[/tmp/.X11-unix]
└─$ ll
总用量 0
lrwxrwxrwx 1 root root 22 2月 16 20:38 X0 -> /mnt/wslg/.X11-unix/X0
srwxrwxrwx 1 shine shine 0 2月 16 20:40 X10
srwxrwxrwx 1 shine shine 0 2月 16 23:04 X11

Then go to the new folder pointed to by device X0
┌──(shine㉿Shadow)-[/mnt/wslg]
└─$ ll -a
drwxrwxrwx 2 root root 60 2月 17 21:26 .X11-unix

┌──(shine㉿Shadow)-[/mnt/wslg/.X11-unix]
└─$ ll
总用量 0
srwxrwxrwx 1 shine users 0 2月 17 21:26 X0

The folder name of Win-Kex socket is .X11-UNIX, whose owner is root user, but the owner of X0 file under this folder is normal user.
I think the reason may be that my normal user doesn't have access to the folder with root permission, so I can't connect to it by normal user

That's on purpose and not causing it.
Does esm mode work for you?

Some additional details + a workaround (which may hopefully lead to finding an actual resolution):

https://github.com/microsoft/wslg/issues/782#issuecomment-1196513933

 sudo umount /tmp/.X11-unix
 sudo rm -rf /tmp/.X11-unix
 sudo ln -s /mnt/wslg/.X11-unix /tmp/.X11-unix

It ?appears? kex is not correctly detecting when /tmp/.X11-unix is a mount, that it's a wslg socket, but does when it's a symlink:

┌──(dhoffman㉿mercury)-[~]
└─$ ls -lart /tmp
total 16
drwxrwxrwx  2 root root    60 Jan 24 14:48 .X11-unix
drwxr-xr-x 19 root root  4096 Jan 24 14:48 ..
drwxrwxrwt  3 root root 12288 Jan 24 14:48 .

┌──(dhoffman㉿mercury)-[~]
└─$ mount | grep .X11
none on /tmp/.X11-unix type tmpfs (ro,relatime)

┌──(dhoffman㉿mercury)-[~]
└─$ kex --status

        Kex Server is stopped.
        Win-KeX SL is stopped.
        Win-KeX ESM is stopped.
        '/tmp/.X11-unix' is a Win-KeX socket          <<<<<<<<<<<<<<<<<<

┌──(dhoffman㉿mercury)-[~]
└─$ ls -i /tmp/.X11-unix/X0
14 /tmp/.X11-unix/X0                   {{{{{{{{{{{{{{{{{{{{{
┌──(dhoffman㉿mercury)-[~]
└─$ ls -i /mnt/wslg/.X11-unix/X0
14 /mnt/wslg/.X11-unix/X0          {{{{{{{{{{{{{{{{{{{{{

┌──(dhoffman㉿mercury)-[~]
└─$  sudo umount /tmp/.X11-unix
 sudo rm -rf /tmp/.X11-unix
 sudo ln -s /mnt/wslg/.X11-unix /tmp/.X11-unix

┌──(dhoffman㉿mercury)-[~]
└─$ ls -lart /tmp
total 16
drwxr-xr-x 19 root root  4096 Jan 24 14:48 ..
lrwxrwxrwx  1 root root    19 Jan 24 14:51 .X11-unix -> /mnt/wslg/.X11-unix
drwxrwxrwt  2 root root 12288 Jan 24 14:51 .

┌──(dhoffman㉿mercury)-[~]
└─$ ls -i /tmp/.X11-unix/X0
14 /tmp/.X11-unix/X0               {{{{{{{{{{{{{{{{{{{{{

┌──(dhoffman㉿mercury)-[~]
└─$ kex --status

        Kex Server is stopped.
        Win-KeX SL is stopped.
        Win-KeX ESM is stopped.
        '/tmp/.X11-unix' is a WSLg socket          <<<<<<<<<<<<<<<<<<

After that kex will move it/back it up automatically when starting up, and will work fine.

┌──(dhoffman㉿mercury)-[~]
└─$ kex

        A WSLg socket exists that prevent KeX from starting.
        Moving the socket now. This will not adversely affect WSL or KeX.

Win-KeX server sessions:

X DISPLAY #     RFB PORT #      RFB UNIX PATH   PROCESS ID #    SERVER
1               5901                            1506            Xtigervnc

You can use the Win-KeX client to connect to any of these displays.

┌──(dhoffman㉿mercury)-[~]
└─$ ls -lart /tmp
total 36
drwxr-xr-x 19 root     root      4096 Jan 24 14:48 ..
lrwxrwxrwx  1 root     root        19 Jan 24 14:57 .X11-unix.bak -> /mnt/wslg/.X11-unix
drwx------  2 dhoffman dhoffman  4096 Jan 24 14:58 tigervnc.KqNxIn
-r--r--r--  1 dhoffman dhoffman    11 Jan 24 14:58 .X1-lock
drwxrwxrwt  2 root     root      4096 Jan 24 14:58 .X11-unix
srwxrwxrwx  1 dhoffman dhoffman     0 Jan 24 14:58 dbus-hVvk4qweDU
-rw-------  1 dhoffman dhoffman   410 Jan 24 14:58 .xfsm-ICE-U21PZ1
drwxrwxrwt  2 dhoffman dhoffman  4096 Jan 24 14:58 .ICE-unix
drwxrwxrwt  5 root     root     12288 Jan 24 14:58 .

┌──(dhoffman㉿mercury)-[~]
└─$ ls -lart /tmp/.X11-unix
total 16
lrwxrwxrwx 1 root     root        22 Jan 24 14:58 X0 -> /mnt/wslg/.X11-unix/X0
srwxrwxrwx 1 dhoffman dhoffman     0 Jan 24 14:58 X1
drwxrwxrwt 2 root     root      4096 Jan 24 14:58 .
drwxrwxrwt 5 root     root     12288 Jan 24 14:58 ..

You can restore it after if you really need to:

┌──(dhoffman㉿mercury)-[~]
└─$ ls -lart /tmp
total 20
drwxr-xr-x 19 root     root      4096 Jan 24 14:48 ..
lrwxrwxrwx  1 root     root        19 Jan 24 14:57 .X11-unix.bak -> /mnt/wslg/.X11-unix
drwxrwxrwt  2 dhoffman dhoffman  4096 Jan 24 14:58 .ICE-unix
lrwxrwxrwx  1 root     root        19 Jan 24 15:00 .X11-unix -> /mnt/wslg/.X11-unix
drwxrwxrwt  3 root     root     12288 Jan 24 15:00 .