Since Chrome OS 118.x, it is not possible to cast via Chromecast from a Chromebook to the TSx G1. If you can connect, the screen briefly goes black and then goes back to the input channel.
We are still investigating this problem. A temporary solution is to reset the Chromebooks to Chrome OS 116:
https://support.google.com/chrome/a/answer/12569990?hl=en&sjid=9876210995098628641-EU