Hetzner dropped support for FreeBSD installs in June/July 2022 according to this post.
Purchase a USB addon drive, and request support write FreeBSD-13.1 install image to it. Give support the link and details in the addon request.
Ole's post covers downloading a prebuilt mfsBSD-13.1.img file into the rescue console, and then using dd to overwrite the first hard drive.
A similar approach is covered in this blog post by the author of mfsBSD.
click0's post covers using an old statically compiled qemu binary (qemu-system-86_64, QEMU emulator version 2.2.0) to load up a mfsBSD iso file, and attach hard disks, from within the rescue system.
This will open SSH on port 1022 and allow connecting with user/pass and running basic commands, including zfsinstall.
This approach is the inspiration for this service, and required a little housekeeping to make it work.
"code for building a FreeBSD disk image which will boot into memory, configure the network, set a root password, and enable SSH.
This can be used to "depenguinate" a Linux box, without requiring any access beyond a network connection.".
It was released in December 2003. A newer version, The Depenguinator, version 2.0 was released in 2008.
mfsBSD is a small boot image which can fit in PXE environments, thumbdrives and used as installer. It is based on the ideas of the depenguinator project.
This script uses a consumer of mfsBSD, with customisations and improvements to security. It provides a single command FreeBSD-13.1 installation via web.