This may be an unsual method but I discovered an issue with the permissions pass through when I was trying to "install" arch to a subvolume using ubuntu 22.04 wsl as the intermedary.

I first installed a basic arch chroot inside of ubuntu using https://github.com/wick3dr0se/archstrap

then i remounted the drive letter that contains the btrfs subvolume using the command sudo mount -t drvfs j: /tmp/archrootfs/mnt/j

then from there I first tried pacstrap -K /mnt/j/@arch base linux linux-firmware

that command threw up this unrecoverable error

error: could not open file /mnt/j/@arch/var/lib/pacman/sync/download-ePxpAU/core.db.part: Permission denied
error: failed to setup a download payload for core.db
error: failed to synchronize all databases (failed to retrieve some files)

the download folder never shows up.

However you can bypass the above issue in a probably really really broken way.

First you copy the db files using cp /var/lib/pacman/sync/* /mnt/j/@arch/var/lib/pacman/sync

then you can kind of install packages via this command.

pacman -r /mnt/j/@arch -S base 

The installation will eventually "fail" with errors such as

( 1/11) Creating system user accounts...
call to execv failed (Permission denied)

This is where the main issue appears.

The entire Executable column is not filled in and it cant be fixed by running chmod -R +x /mnt/j/@arch/usr/bin

the correct permissions should probably be something like this

However you can fix it if you open each executable individually and manually apply the executable permissions bit.

But doing this for every file in /usr/bin and other directories which contain executables is ... possible todo but extremely time consuming.

Plus I dont know if the user and group values will even allow it to boot.