To use Anytype local-only without the sync to Anytype servers, the setting is only available on the initial login screen gear icon on the top right corner (on both desktop and mobile). So you might have to logout first, if you started using Anytype before the option for local-only was available.
My first Anytype video tutorial
Please let me know what other videos you would like to see, or how I can improve the content.
Thanks @Code-Jack! I must confess that I make training materials for my day job
I have faith that official onboarding and videos will get better with time, as it is hard to do when features are changing quickly in beta.