Cannot find package knex on production build of nuxt server (api routes)

Forwarded from downstream issue: https://github.com/nuxt/nuxt/issues/22373 by @bvqbao

Environment

• Operating System: Windows_NT
• Node Version: v18.16.0
• Nuxt Version: 3.6.5
• Nitro Version: 2.5.2
• Package Manager: npm@9.5.1
• Builder: vite
• User Config: devtools, modules, content, experimental
• Runtime Modules: @nuxtjs/tailwindcss@6.8.0, @nuxt/content@2.7.2, @nuxtjs/eslint-module@4.1.0
• Build Modules: -

Reproduction

https://github.com/bvqbao/nuxt3-module-notfound

Describe the bug

I have created some API in ~/server/api. The API use knex package to access to an SQLite DB.
In dev mode (npm run dev), the API work as expected:

However, when I build the server for production (npm run build) and run the server (npm run preview), the server returns an error about "Cannot find package ..." knex, altho it is present in ./output/server/node_modules:

I don't use TypeScript but JavaScript in ~/server.

Additional context

No response

Logs

No response

Start with the linked reproduction repository and compare npm run dev with npm run build followed by npm run preview, focusing on the API under ~/server/api and the generated ./output/server/node_modules. Check the forwarded Nuxt issue for current context; done means the production server can load knex and serve the SQLite-backed API without the package error.