Use the command palette to pick "agent: toggle" - that'll open the agent pane. Pick "Claude Agent" from the dropdown at the top if you see the Zed agent. Should be all you need.
Their ACP integration with Claude agent is extremely broken to the point of being almost unusable. It desyncs and breaks in other ways constantly requiring frequent IDE relaunch. I get that they want you to use their built-in agent but $200 Codex/CC plans are such a good deal it makes very little sense atm and the broken integration is just embarrassing...