How can I automatically tag users and leads when a conversation is closed?

Hi all! We're attempting to set up a flow by which Users/Leads are tagged with a specific tag when a conversation with them is closed (that tag is then used to add them to a Series).

I'm not seeing a rule trigger that supports this flow. Would we need to set up a custom app with the conversation.closed webhook topic? Or anyone have a good workaround for what we'd like to do, which is "when conversation closed, tag user with X"? Thanks!