I'm trying to deploy a Nuxt 4 project which works, but functions folder is not being served

// wangler.toml
name = "<project>"
compatibility_date = "2025-09-29"

main = "functions/api/worker/index.js"

[site]
bucket = ".output/public"

// wangler.toml
name = "<project>"
compatibility_date = "2025-09-29"

main = "functions/api/worker/index.js"

[site]
bucket = ".output/public"

// functions/api/worker/index.js
import { getAssetFromKV } from "@cloudflare/kv-asset-handler"
import * as auth from "./auth.js"
import * as callback from "./callback.js"

export async function onRequest(context) {
  const url = new URL(context.request.url)
  const pathname = url.pathname

  // Handle API endpoints
  if (pathname.startsWith("/api/worker/auth")) {
    return auth.onRequest(context)
  }

  if (pathname.startsWith("/api/worker/callback")) {
    return callback.onRequest(context)
  }

  // Everything else serves the static site
  try {
    return await getAssetFromKV(context)
  } catch (err) {
    // If not found, fall back to SPA index.html
    if (err.status === 404) {
      return await getAssetFromKV(context, {
        mapRequestToAsset: (req) =>
          new Request(`${url.origin}/index.html`, req),
      })
    }
    throw err
  }
}

// functions/api/worker/index.js
import { getAssetFromKV } from "@cloudflare/kv-asset-handler"
import * as auth from "./auth.js"
import * as callback from "./callback.js"

export async function onRequest(context) {
  const url = new URL(context.request.url)
  const pathname = url.pathname

  // Handle API endpoints
  if (pathname.startsWith("/api/worker/auth")) {
    return auth.onRequest(context)
  }

  if (pathname.startsWith("/api/worker/callback")) {
    return callback.onRequest(context)
  }

  // Everything else serves the static site
  try {
    return await getAssetFromKV(context)
  } catch (err) {
    // If not found, fall back to SPA index.html
    if (err.status === 404) {
      return await getAssetFromKV(context, {
        mapRequestToAsset: (req) =>
          new Request(`${url.origin}/index.html`, req),
      })
    }
    throw err
  }
}

// my 2 functions open with
export async function onRequest(context) {
...

// my 2 functions open with
export async function onRequest(context) {
...

// package.json
  "scripts": {
    "submodules:init": "git config --global url.\"https://${github_PAT_TOKEN}@github.com/\".insteadOf \"https://github.com/\" && git submodule update --init --recursive",
    "nuxt:build": "pnpm install && pnpm generate",
    "build:cloudflare": "pnpm run submodules:init && pnpm run nuxt:build",
    "deploy:cloudflare": "npx wrangler deploy",

// package.json
  "scripts": {
    "submodules:init": "git config --global url.\"https://${github_PAT_TOKEN}@github.com/\".insteadOf \"https://github.com/\" && git submodule update --init --recursive",
    "nuxt:build": "pnpm install && pnpm generate",
    "build:cloudflare": "pnpm run submodules:init && pnpm run nuxt:build",
    "deploy:cloudflare": "npx wrangler deploy",