Using the Wayback Machine's Save Page Now interface, you can now also save outlinks (linked pages).
A quote from the original 2019 announcement:
You can now save all the “outlinks” of a web page with a single click. By selecting the “save outlinks” checkbox you can save the requested page and also all linked pages
The Wayback Machine's Save Page Now interface can be used without an account however extra features like saving outlinks, saving screenshots, and saving pages to your my web archive all require signing in.