<title>title</title>
<button onclick="history.pushState({}, 'new title', 'other.html')">click me</button>

I tested this in Chrome, Edge, Firefox and Safari (Desktop) and none update the tab title.

https://html.spec.whatwg.org/#dom-history-replacestate says "The title is purely advisory. User agents might use the title in the user interface" but if it never does anything, some action is needed.

Is this a feature worth trying to save? If so we need to file bugs and see if we can make it happen. If not, then we should probably make this argument explicitly a dummy and recommend using document.title instead.

See also http://stackoverflow.com/questions/13955520/page-title-is-not-changed-by-history-pushstate