Hello shavrlis, welcome to the community!
Thank you for posting the logs of your Shake. From them, it appears that there is no data transmission between the blue Shake board and the Raspberry Pi board:
2020 365 17:45:40: Setting Serial Port Name: HW Revision: a02082 / Port Name: /dev/ttyS0
2020 365 17:45:57: Unable to read Firmware version number off of Serial Port /dev/ttyS0 after trying for 15 seconds, cannot continue!
2020 365 17:45:57: Is the Pi computer connected to the Raspberry Shake Board? Please confirm and try again.
Did you assemble the Shake yourself? Even if you received a pre-assembled unit, can you please check that every cable is properly in its socket, and that the Shake blue board is solidly inserted in the Raspberry Pi computer pins?
We will proceed forward once these checks are done.