windows.remove()

var removing = browser.windows.remove(
  windowId        // integer
)

function onRemoved() {
  console.log(`Removed window`);
}

function onError(error) {
  console.error(`Error:`, error);
}

browser.browserAction.onClicked.addListener((tab) => {

  var removing = browser.windows.remove(tab.windowId);
  removing.then(onRemoved, onError);

});

// in a script loaded by the page in the window
document.querySelector('#close').addEventListener(async ({ button, }) => { try {
  if (button) return; // not a left click
  const windowId = (await browser.windows.getCurrent()).id;
  await browser.windows.remove(windowId);
  // this point will never be reached, since the window is gone
} catch (error) { console.error('Closing failed:', error); } });