If you just want to copy a few files out of Ubuntu, then you can certainly use the \\wsl$\Ubuntu method that @Android776 propose in the other answer. However, that will pretty much only work properly for files that your Linux user created and owns. Other files will lose their permissions and/or owner (typically root), and some system files won't be readable at all that way, (e.g. /etc/shadow).
Since you say that you want to move the Docker data over to the new laptop, you're going to need to use the --export method described below anyway, so you might as well use it for both the Ubuntu filesystem as well as that of Docker.
Backing up is the easy part -- WSL provides the ability to export a distribution, which creates a tar file that can then be imported again, either on the same computer (as a new distribution) or on another system.
I'm going to assume that your USB drive is D:, but substitute whatever drive letter you need below.
From PowerShell:
wsl --export Ubuntu D:\ubuntu.tar
wsl --export docker-desktop-data D:\docker-desktop-data.tar
There's no need to export docker-desktop, since it will be automatically re-created properly when you install Docker Desktop on the new laptop.
Eject the USB drive (properly, using the Eject command from the taskbar) and move it to the other computer.
On Windows 11 on the new computer:
Start an Admin PowerShell.
wsl --install (if you haven't already)
Reboot when told.
Complete the installation, which will install a new Ubuntu -- You won't use this one.
Remove this newly installed Ubuntu. From a non-Admin PowerShell:
wsl --unregister Ubuntu
Important: Only do this on the new computer, and only immediately after installing this way. This will remove all files from the newly installed Ubuntu version.
Next, we restore the Ubuntu distribution that we backed-up to the USB drive. Attach the USB drive (again, assuming D:).
Again, from a non-Admin PowerShell:
# Adjust paths and names below as desired
mkdir $env:USERPROFILE\WSL\instances\Ubuntu_WSL2
wsl --import Ubuntu_WSL2 $env:USERPROFILE\WSL\instances\Ubuntu_WSL2 D:\ubuntu.tar --version 2
wsl --set-default Ubuntu_WSL2
wsl ~
Note that you need to name the new Ubuntu something besides "Ubuntu", or "Ubuntu-20.04", etc. These are the names used by the Store installer, and this installation will be "separate" from that. It's better to not "confuse" the Store installers if you do ever run them again (on purpose or accidentally).
From within this Ubuntu, all your files should be present, but you'll be root instead of your normal user. You need to set the "default" user by:
sudo -e /etc/wsl.conf
And add:
[user]
default=your_username
your_username should be the username you were using on Ubuntu on the old laptop.
Now exit
And restart WSL, and you should be back to normal
Let me know how that works out for you, and I'll work on adding directions for restoring docker-desktop-data as well.