TLDR: use browser.proxy.onRequest.

MDN doc about the firefox's proxy API, it's quite different from chromium's chrome.proxy.

use browser.proxy.onRequest.addListener(listener, {urls:['<all_urls>']}) to get requestDetail.
usually, the requestDetail.documentUrl of extension request is in format like: moz-extension://${internalUUID}/path
listener returns an invalid proxy to block request 🤣

internalUUID is unique for each extension, but it's different from the extension id returned by browser.management.getAll(), and I can't find a way to get it in extension.
one way to get internalUUID is, open this page about:debugging#/runtime/this-firefox, run some snippet in devtool:

const idPairArr=[];
for(let card of document.querySelectorAll('.card')){
  const fields = card.querySelectorAll('dd.fieldpair__description');
  if(fields.length>=2){
    idPairArr.push({
      extensionId:fields[0].innerText,
      internalUUID:fields[1].innerText
    })
  }
}
console.log(idPairArr);

related issues: #8, #14