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Thank you for your help. But I checked my chrome dev tools and it is not a problem with local storage, the flow and results are showed in these screnshots.

This is the http api request when I do manual testing. Notice at the end of Response headers how Set cookie sets appSession.

In the Cypress command, this is when it fails. No Set-Cookie response header. However, the remote addresses are not the same in General properties. 🤔