Thank you for this article and the comments.

Reading here and there, the solution I came with is:

sudo umount /mnt/c
sudo mount -t drvfs C: /mnt/c -o metadata

To make the change permanent, edit /etc/wsl.conf:

options = "metadata,uid=,gid="

To use the config file in ssh, I simply restrict the permissions on this file to read-only on Windows.