Copilot studio Agents published on Sharepoint

Hi everyone,
I'm hoping someone can confirm or correct my understanding of a limitation we're experiencing.
We have a Copilot Studio agent published to a SharePoint site. When users interact with the agent, they are unable to see their previous chat history — unlike the built-in SharePoint AI agents (e.g. SharePoint Agents / Copilot for SharePoint), which do appear to retain and display conversation history.
Is it correct that Copilot Studio agents published to SharePoint do NOT support persistent chat history visible to the end user, while native/built-in SharePoint AI agents do support this out of the box?