Apple review requires a test account login path that doesn't depend on
Google OAuth. Add amazon-cognito-identity-js for direct SRP auth with a
native email/password form on the login screen. Fill in the empty Cognito
client ID and pool ID, fix the Cognito domain prefix, and align CDK
callback URLs with the app's actual URL scheme. Enable push-triggered
mobile deploys, add CDK outputs for client IDs, fix stale README
references, and add mobile/README.md.
