The three currently-maintained engines which (at their feature intersection) effectively define what "the web" is today are Mozilla's Gecko, Apple's WebKit, and Google's Blink.

The latter two are both descended from KHTML, which came from the Konquerer browser which was first released as part of KDE 2.0 in 2000, and thus both are LGPL licensed.

After having their own proprietary engine for over two decades, Microsoft stopped developing it and switched to Google's fork of Apple's fork of KDE's free software web engine.

Probably Windows will replace its kernel with Linux eventually too, for better or worse :)

How else are Chrome, Edge, Brave, Arc, Vivaldi and co getting away with building proprietary layers on top of a copyleft dependency?

They're allowed to because the LGPL (unlike the normal GPL) is a weak copyleft license.