Minecraft App Authorization

Make sure you have authorized Minecraft to access your info in the popup. Achievements require it

Hey there, Evie Jinks

Did you try and see if the Microsoft account is shown in your authorized apps on your PSN account: How to manage authorized apps on PlayStation (US)?

Nathan

Sorry but only authorized apps can be installed on the console. These apps can be found in the apps store.

It might be looking for authorization to link your account. I'm not sure that you can manually add the "approval", there are APIs that the app should be using to ask to access parts of your Microsoft Account and prompt you for that authorization. You
can check what is currently authorized for your account at your Microsoft Account page,
clicking on Privacy at the top, then scrolling down on that page to the part for "Apps and services that can access your data". That page will have a list of apps that are authorized to access your Microsoft account.

Do you have two factor authentication set up on your account? It might be prompting on another device for authorization if so.

Are you doing this in a world, or is this during the setup process before you start saving?

Edit: forgot to link to the Minecraft on Switch FAQ
which has some answers for troubleshooting problems that might help in this situation.