Had this exact thing happen in production when we turned off an audit DB replication slot. We got lucky and caught it before our entire app went down. It’s one of the many foot-guns we have found with Postgres.
I'm not sure telling a replication system to keep copies of all changes without limits until they're replicated and then not letting them replicate is much of a footgun. You're getting exactly what you asked for and any system with the setup is going to eventually start filling up space if the replication or connector goes down. It's like complaining that your kitchen floor got wet when when you plugged the sink and left it running - it's unpleasant surprise, maybe you wanted a sink with an emergency overflow outlet, but it's the obvious outcome.