You don't have to store the nonce in a cookie, they just say that you have to be able to link it back to the original request, how you store the value is up to you.
Your app, if it is an embedded app within the Shopify admin, needs to be able to work with 3rd party cookies turned off. E.g. in Incognito mode with block 3rd party cookies turned on. In this case you will not be able to set cookies in the browser or use local storage or anything like that.
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