Upgrade Sakai template to Nuxt 4.1 and PrimeVue 4 with official module support, fix Vercel deployment, and apply Nuxt 4 best practices

[who-jonson]

Summary

Upgrade this repository from the current Sakai/Nuxt setup to modern Nuxt 4.1 + PrimeVue 4 using official Nuxt module integration, resolve Vercel deployment issues, and align the project with Nuxt 4 best practices.

Goals

Upgrade to Nuxt 4.1
Upgrade to PrimeVue 4
Use official PrimeVue Nuxt module support
Fix Vercel deployment/build issues
Apply Nuxt 4 best practices across config and app structure

Scope

Dependencies and compatibility updates
Nuxt config/module integration updates
PrimeVue setup migration to module-based configuration
Vercel build/runtime configuration fixes
Cleanup/refactor for Nuxt 4 conventions (where needed)

Acceptance Criteria

App runs locally on Nuxt 4.1 without regressions
PrimeVue 4 components/theme integration works via official Nuxt module
Vercel deployment succeeds with no build/runtime errors
No critical lint/type/build errors
Key pages/layouts render correctly after migration

Notes

Keep changes minimal and focused on migration + deployment reliability.
Document any required env/config changes for Vercel.