The issue was not present on Fedora 40 (GNOME 46) or Fedora 41 (GNOME 47) running off a USB stick. The issues popped up after upgrading to Fedora 41 from 40.
For me this worked on a fresh Fedora 41 install up until a few days ago, presumably when I last updated.
I’m experiencing the same exact issue, with the call answer/hangup keys on a ThinkPad. Key events are working just fine, as checked with wev and sudo libinput debug-events.
The issue seems to be with the Settings app itself not handling these keys properly, as manually editing the settings in terminal or with dconf-editor (/org/gnome/settings-daemon/plugins/media-keys/play for the Play/Pause action) to the key (XF86PickupPhone in my case) works. For now, this is a workaround for experimented users. The related issue also talks about this.
But for me, this doesn’t explain why the setting itself was cleared/broken when the update occurred.