Emacs with xwidgets support needs webkit2gtk-4.0, which for us means the variant built with libsoup2 on core-updates-frozen. I've changed the inputs in the two affected Emacs packages and added to the comment about where webkitgtk-with-libsoup2 is used. Apologies if the formatting/style of the commit message is off, wasn't sure how best to do this.
From 17dd0a5748bc4a984393812e395e88c6060cbf55 Mon Sep 17 00:00:00 2001
From: John Kehayias <firstname.lastname@example.org>
Date: Sat, 20 Nov 2021 14:03:08 -0500
Subject: [PATCH] gnu: emacs-xwidgets/-next-pgtk: Replace webkitgtk with
* gnu/packages/emacs.scm (emacs-xwidgets and emacs-next-pgtk)[inputs]: Replace
webkitgtk with webkitgtk-with-libsoup2.
* gnu/packages/webkit.scm (webkitgtk-with-libsoup2): Add further information
about where this package is used and upstream tracker for libsoup3.