We have this same problem 😔.
We followed the quickstart: https://fusionauth.io/docs/quickstarts/quickstart-javascript-react-web.
Like @richard-0, the only difference is we use a hosted FusionAuth instance (that is working well for our Laravel app).
The response is the same: missing_response_type
Going over the SDK it seems that there is no response_type parameter.
The SDK needs to be updated. Can you guys look into that?
Also: I am fairly confident that when I tried to set this up earlier this year, that it did work. So I have feeling this was changed fairly recently.