Did you try out uninstalling the preinstalled GNOME Web and installing it as Flatpak? Flathub has a much newer version available afaik.
Also as a hint: WhatsApp For Linux is an unofficial WhatsApp Web client for Linux using WebkitGTK (as GNOME Web). They have a hint in the linked wiki page that they were not be able so far to trick the WhatsApp Server to assume another user agent as Safari.
Maybe WhatsApp for Linux could also be an alternative for you? Unfortunately, I was not able to launch it as the application crashes on start on my Librem 5. So I also cannot tell you, wether it is scaling better than the Web Version itself (with help of any CSS hacks or so).