I was having a similar issue:

Uncaught (in promise) SyntaxError: The requested module '/_nuxt/node_modules/@supabase/supabase-js/node_modules/@supabase/postgrest-js/dist/cjs/index.js?v=4c501d24' does not provide an export named 'default' (at wrapper.mjs?v=4c501d24:1:8)

The only thing that finally cleared up this error for me was adding this in my nuxt.config.ts

  vite: {
    optimizeDeps: {
      include: [
        "@supabase/postgrest-js",
      ],
    },
  },

Not sure if this will be helpful since it's not exactly the same issue. I'm fairly new to Nuxt, so I can't really give a good explanation for why this works on my end. Happy coding!