Hi @Felix,
Within the web-channel as well, any person must be identified in order to send an in-app message and it is not possible to send a message to an anonymous person at the moment. The reason for this is currently, in-app messages are triggered based on specific events/attributes that is specified within the campaign or broadcast, etc all of which requires a person to be identified in order for the correct message to be sent to the correct person.
I believe what you’re looking to do is to send a web/in-browser push notification. We have an open request for a feature like this that our team is tracking feedback on and I have upvoted it on your behalf so that our product team knows this is something that would be useful to you.
Apologies I don’t have any better news for you today Felix but I hope this helps to clarify!