Sign in at parler123.app with the same Google or Apple account you use in the app. Your children, books, cast and pictures are all there.
On the web you can write and read stories, read captured pages, manage children and sign-in codes, invite family and manage billing. Some newer features (routines, cast approvals and class iPads) are in the iPhone and iPad app first.
If you started a subscription in the App Store, manage it there; web subscriptions are managed from Billing on the web.