Hi @phoebe,
Thanks for using FusionAuth!
Did you get this resolved? We have a simple react application tutorial here which uses the react SDK. I'd be interested in knowing if deploying that application to Azure SWA has the same issue.
If it does, then maybe there's some additional configuration that needs to be set or a change to the React SDK that is needed. If it doesn't, maybe there's an issue with the react app you wrote.
Also, are you seeing any messages in the JavaScript console?