You might have overwritten
/etc/passwd when you did
pacman -S --force shadow. Trying to log in on a virtual console (i.e., tty for keyboard and HDMI monitor) or the serial port (UART connected to some of the GPIO pins) will be no more successful.
Remove the SD card from the Raspberry Pi, insert it into another computer running Linux and with shadow (so likely any relatively modern distro), and either:
Sync and unmount the SD card, then put it back in the Pi and try booting from it.
Other users on the Raspberry Pi might have been fudged or completely missing too.
Logging in over SSH should change nothing versus logging on the console if you overwrote
Follow important Arch Linux news. The most recent would have saved you the grief. All binaries in
/usr/sbin got moved to
/usr/bin and you still have something thereunder, hence why pacman is complaining. Follow the instructions in that article but use your judgement. If they don't fix the problem entirely (you are in an unclean state after all), you may be able to get away with manually moving everything in
/usr/bin and trying again.
Do not use
--force unless you know what you are doing or explicitly told to do so by Arch devs.