I think I'm able to fix your problem from the code sandbox.

https://codesandbox.io/p/devbox/bold-field-dcjmhn

What I did was to downgrade the pinia from 3.x to 2.x. I don't know the specifics, but I also had problem working with pinia 3.x with Nuxt, so I went with 2.x instead. I've also updated @pinia/nuxt and the nuxt version itself for compatibility.

I've also modified the app.vue so that you can see the store being modified in realtime.

Sorry that I can't give you the detailed reason behind this error.