Download the x86_64 "Mini root filesystem" tarball from https://alpinelinux.org/downloads/.
curl -LO https://dl-cdn.alpinelinux.org/alpine/v3.21/releases/x86_64/alpine-minirootfs-3.21.3-x86_64.tar.gz
Check that the hash matches.
Get-FileHash -Algorithm SHA256 alpine-minirootfs-3.21.3-x86_64.tar.gz
Install from the rootfs tarball.
wsl --install --name Alpine --from-file alpine-minirootfs-3.21.3-x86_64.tar.gz
Enter a root shell. You can also close and reopen Windows Terminal and Alpine should be added to the list of profiles.
wsl.exe -d Alpine
Add a new user. Add yourself to wheel group so you can use doas become root temporarily.
adduser -h /home/avery -s /bin/ash avery
adduser avery wheel
Install and configure doas.
apk add doas
echo "permit :wheel" >> /etc/doas.conf
Back in PowerShell, set the default user.
wsl --manage Alpine --set-default-user avery