bluetooth a2dp sink does not work with pulseaudio clients

I have a bluetooth headset connected to PipeWire with the A2DP profile enabled. While I can play audio just fine on this headset with pw-play, pipewiresink, aplay -Dpipewire, jack clients, etc... it doesn't work with PulseAudio clients (paplay, pulsesink, etc). The client connects and links to the a2dp sink node, but it looks as if the clock is not running.