After asking for some help on #pipewire channel, I could make pipewire work again by creating the following file:
$ sudo touch /etc/pipewire/media-session.d/with-pulseaudio and restarting pipewire service. This bug can be closed, but it would be better if there was a changelog (apt-listchanges) mentioning the removal of this file, which is necessary even if I don't have pulseaudio in this system.