I do something very similar, also with Claude and Codex, because the workflow is controlled by me, not by the tool. But instead of plan.md I use a ticket system basically like ticket_<number>_<slug>.md where I let the agent create the ticket from a chat, correct and annotate it afterwards and send it back, sometimes to a new agent instance. This workflow helps me keeping track of what has been done over time in the projects I work on. Also this approach does not need any „real“ ticket system tooling/mcp/skill/whatever since it works purely on text files.
semantic plan name is important
+1 to creating tickets by simply asking the agent to. It's worked great and larger tasks can be broken down into smaller subtasks that could reasonably be completed in a single context window, so you rarely every have to deal with compaction. Especially in the last few months since Claude's gotten good at dispatching agents to handle tasks if you ask it to, I can plan large changes that span multilpe tickets and tell claude to dispatch agents as needed to handle them (which it will do in parallel if they mostly touch different files), keeping the main chat relatively clean for orchestration and validation work.