Dependency failed for Local File Systems after December update

Because the image is not broken.

There is a compatibility issue with a very small percentage of SD cards with the new sdhost driver in the December update which is being investigated, however this is not the problem you’re having. You have dtoverlay=mmc in config.txt and I can confirm from your system journal that sdhost is not being used therefore your issue is nothing to do with the sdhost issue reported in this thread.

What I do see however in your log is this:

Dec 30 19:06:41 osmc systemd[1]: Job dev-sda1.device/start timed out.
Dec 30 19:06:41 osmc systemd[1]: Timed out waiting for device dev-sda1.device.
Dec 30 19:06:41 osmc systemd[1]: Dependency failed for /media/usb_hd.
Dec 30 19:06:41 osmc systemd[1]: Dependency failed for Local File Systems.

OSMC is unable to mount your external USB drive, and because you do not have the ‘nofail’ mount option in fstab for the external drive, this prevents the entire system from booting.

You can fix this by adding ‘recovery’ to your /boot/cmdline.txt which will let you boot to an emergency recovery console, then edit /etc/fstab and add the nofail mount option for that drive, then remove ‘recovery’ from cmdline.txt and reboot and you should find you can now boot.

Then you can investigate the problem with your external drive.