Dear Maintainer, sending a file from a paired and trusted mobile device to a Debian KDE desktop fails even when the configuration item is set to "Always accept".
So, as it was said in #1123793, manually deleting /usr/share/dbus-1/services/org.gnome.evolution.dataserver.Sources5.service makes bluetoothd pick up OBEX services again, so file receiving now works. This bug is probably should be closed.
By further researching, the issue is that bluetoothd doesn't add OBEX profiles to the controller capabilites until obexd starts, which happens only at KDE login (as obex needs D-Bus etc). So if bluetoothd is restarted manually after login, it picks up OBEX and everything works. The bug #1123793 in bluez is probably related to it.