This is a known issue for certain types of module.
If a module has some sort of global control on Rack, then it typically guards against multiple instances having an effect.
I had a similar issue with Purfenator module that displays .vcv patch name - #8 by ale47p which I think should work correctly.
BrightIdea is one of my older modules, so it hasn’t been updated with new code yet.
It is somewhere on my TODO list, but not at a particularly high priority.
What is the use-case that you need BrightIdea to work for multiple DAWs?