Chrome Extension: console log in page console, not in extension console

log.js

// returns current tab
const getCurrentTab = async () => {
  const [tab] = await chrome.tabs.query({ active: true, currentWindow: true });
  return tab;
}

// log to current page console
const log = async (...arguments) => {
  const tab = await getCurrentTab();

  chrome.scripting.executeScript({
    target: { tabId: tab.id },
    func: (...arguments) => {
      console.log('[from extension]', ...arguments);
    },
    args: arguments,
  });
}

// logs go to extension console
console.log('log in extension console');

// logs go to page console
log('log in page console');