only with the current alpha or has this shown in older versions before? (I have never seen such a message, but could be related to a change in the latest build)
//edit ah sorry, I misread 4.403 as 4.409. In that case I'd say it's not a BTT problem you are seeing because 4.403 is already installed on many machines. When doing a quick Google search I found many posts about error 609 for various apps out there, most suggest a system restart will fix it.
I had a closer look. The error mostly seems to appear when a Apple Script doesn't receive a response from the queried application. For example if the other application has crashed / frozen.
Can you think of any Apple Scripts running in BTT? Maybe for Touch Bar or Floating Menus?
If it happens again, possibly go to help => export diagnostic debug information in BTT and send the result to me (andreas@folivora.ai). I'm not sure, but maybe the logs will contain some useful info.