Here’s my code that loads the pdf library and setup workerSrc.

import * as pdfjsLib from 'pdfjs-dist';
pdfjsLib.GlobalWorkerOptions.workerSrc = `//cdnjs.cloudflare.com/ajax/libs/pdf.js/${pdfjsLib.version}/pdf.worker.min.js`;

export default defineBackground(() => { 

browser.downloads.onCreated.addListener(function (downloadItem) {
   // download this url and get data
   const pdfDoc = pdfjsLib.getDocument(await blob.arrayBuffer()).promise;
    const pages = (await pdfDoc).numPages;
    console.log("[parseFileContent]: pdf pages: ", pages);

}

}

I also added this code in my config file

export default defineConfig({
  modules: ["@wxt-dev/module-react"],
  manifest: {
    permissions: ["downloads", "webRequest", "tabs", "storage"],
    host_permissions: [
      "*://*.amazonaws.com/*",
      "*://*.amazoncognito.com/*",
    ],
    web_accessible_resources: [
      {
        resources: ["pdf.worker.js"],
        matches: ["<all_urls>"],
      },
    ],
  },
  extensionApi: "chrome",
});

I tried using the code above after searching many stackoverflow questions.