To help me understand your setup better, is it possible to share a test page? From your last 2 screenshots, it appears though you cleared the conversation a new conversation is started automatically? By default this doesn't happen, unless you are subscribing to MessagingService.cleared event and starting a new one. If that is not the case, then I will need to understand more how this is happening.
Also, the error dialog shouldn't be appearing just when switching between the apps. If it appears, it indicates that it failed to restore or reconnect to that conversation.
Best bet would be to reach out to care team who can help debug the use case here and resolve.
Hi @fransiska.hendra, external emails are blocked to us. The process will be to reach out to care team sharing your resources to replicate the issue and will be able to help resolve your concern.