I think I've found a way to get this working. The main issue seems to be that Sonoma's Webkit installation doesn't work with apps that don't have a `CFBundleDisplayName` set. Open this file:
~/Library/Application\ Support/Steam/steamapps/common/Baldurs\ Gate\ 3/Baldur\'s\ Gate\ 3.app/Contents/Info.plist
and change this section:
<key>CFBundleDisplayName</key>
<string></string>
to something like this:
<key>CFBundleDisplayName</key>
<string>BG3</string>
You'll have to re-sign the application because you've edited its contents:
codesign --force --deep --sign - ~/Library/Application\ Support/Steam/steamapps/common/Baldurs\ Gate\ 3/Baldur\'s\ Gate\ 3.app
…and that should get the launcher working correctly again. I've now logged in and even cross saves are loading fine.