I just encountered a sneaky thing I had not seen, although it probably worked in 1999 already. A web site was showing a different title on the tab, depending on it being active or not.

The whole trick is to use the blur and focus event handlers on the window to change the title.

window.onblur = function() {
    document.title = 'Please come back!';
}
window.onfocus = function() {
    document.title = 'You have 6 items';
}

You could also change the favicon that way. Maybe this is a common practice and it feels pretty spammy, but there may be some good use cases for it, too.

If you don't want to clobber other events, it is better to use addEventListener:

let activeTitle = 'You have 6 items';
let inactiveTitle = 'Please come back';
document.title = activeTitle;
window.addEventListener('blur', e => {
    document.title = inactiveTitle;
});
window.addEventListener('focus', e => {
    document.title = activeTitle;
});