The very slow method is to clone the eMMC of an eMMC model (SD card model is trivial since you can just plug it into the host PC), loopback mount the image, change it, then reflash using the updated clone image.
Note: Device mode is not “present as a storage device” unless it was programmed that way. A recovery mode Jetson is a custom device, so there is no possibility of doing this even with programming. Programming would require the system to be booted. If you have failures, then it is generally best to have a recovery boot entry and to pick that with a serial console during boot.
Individual files use ssh for file copies (e.g., scp, sftp, or a number of file backup utilities). All of those (other than entire partition clone) require a fully running system.