Personally tested it and it works!
I have to run four to five scheduled tasks almost every day.
After about three or four days, the task list on the left side of my Codex will be filled up with the content of these scheduled tasks, causing some historical tasks that I have specially reserved before to be squeezed out.
You can try this for your Codex app.
It says: "Only keep the latest xxx task, and archive the others.
Remember this choice." Isn't it very practical?
You can also actively ask Codex to organize and archive the history related to a certain topic, like in the video below.