The Kukai embed feature is a secure way to sign up for a wallet address and generate an authentication message. Unfortunately, access to the Kukai embed feature is limited and currently only allows for login. If you need to gain access to the feature for anything more than login, it is not currently possible. However, if you have any questions or need help with the allowlisting process, you can email Jarrod at jarrod@kukai.app for assistance.
Right now and for the foreseeable future access to Kukai emded for anything more than login is limited. If any at all, It won't be possible for more feature access than login ( its solely for signup, generating a wallet address, and in that flow signing an authentication message ).