Hello guillochon,
Thank you for contacting us about this issue you are experiencing between the Shake and the Pi4 board. From what you have written (blue light on, red light on, green light blinking in that particular way) it indeed seems that the board revision is still not supported by our Shake OS.
This is the complete list of supported RaspberryPi board revisions for each one of our Shake models, could you please check if yours is in this list? Technical Specifications — Instructions on Setting Up Your Raspberry Shake
If it is not, we will need to wait until we can acquire one of these newer units to be able to get our image updated to work with the latest versions of rPi, and with the current shortages, this could, unfortunately, take a while.
However, another user has experienced a similar issue, and has managed to solve it with a bit of a creative approach. You can see it here Support for Raspberry Pi 4 Model B (d03115) - #6 by Uxyll and maybe this procedure will be of help.