Hi Lindsay,
I think that you can just put the conversation ID in the URL in the web app to go straight to it:
https://apps.mypurecloud.com/directory/#/engage/admin/interactions/CONVERSATIONIDHERE
For example,
https://appsmypurecloud.com/directory/#/engage/admin/interactions/a658968b-321c-4043-bcef-95b5a6ac78c7
As far as I know, there isn't a way to search by conversation ID through the UI. Hopefully someone will correct me if I'm wrong!