FWIW Brave does that. If you reach a page with a 404 a banner will appear on top with a button to try and navigate to the latest version of the page you're looking for at the archive.
There's an official Wayback Machine extension for Chrome:
Except it very often misdetects a successful load of a page as an error and redirects you away.
Really? It's not done that to me yet. It just pops up a 'see this page on the wayback machine' dialog, which I can dismiss if I want.
There's a fantastic extension for Firefox, Chrome, etc. called Web Archives which will attempt to find a copy of the missing page from the Wayback Machine, Google Cache, Archive.is and many more.