the login flow is quite straight forward and much of the expirience depends on the OpenID connect provider the backend is trusting.
You can go to https://monsterwriter.com/ and see the system in action. When you click on login you will be redirected to a login provider, which in case of MonsterWriter is auth0. But it could also be an open source (e.g. KeyCloak) or any other commercial OIDC provider. Then it is up to the OIDC provider to display the "login with Google"
The hello world example on the website provides a dummy OIDC provider, If you try out the hello world example I guess this is the best place to really get an idea: https://linkedrecords.com/getting-started/
I tried your monsterwriter site (nice looking app, by the way), and logged in with google. I don't see any option to "control where my data is stored". As far as I can tell as an end user, I've just created an account on your site.
Reading the Getting Started code, it only shows me configuring storage as a developer. Nothing about users doing any sort of bring-your-own storage, let alone firing one up from scratch with a friendly workflow.
What am I missing?