This python3 script randomly chooses an output device and tells pulse audio to bind ALL the outputs from all the programs to that device.

paclientbind.py

#!/usr/bin/python3
import subprocess
import random


# get a list of all available sinks (output-devices)
get_the_sinks = subprocess.check_output(["pactl", "list", "short", "sinks"]).decode('utf-8').split("\n")
list_of_sinks = []
for outputline in get_the_sinks:
	this_sink_listing = outputline.split("\t")
	if (this_sink_listing != ['']):
		list_of_sinks.append({'id':int(this_sink_listing[0]), 'name':this_sink_listing[1], 'driver':this_sink_listing[2], 'sampling':this_sink_listing[3], 'state':this_sink_listing[4]})


# get a list of all running outputs (like... programs)
get_the_sources = subprocess.check_output(["pactl", "list", "short", "sink-inputs"]).decode('utf-8').split("\n")
list_of_sources = []
for outputline in get_the_sources:
	this_source_id = outputline.split("\t")[0]
	if (this_source_id != ''):
		list_of_sources.append(int(this_source_id))

# choose ONE sink… here it is done randomly but it could also be set by a regexp on the sinks name or hardcoded by its ID or whatever

target_sink = random.choice(list_of_sinks)['id']


for source_id in list_of_sources:
	subprocess.run(['pactl', 'move-sink-input', str(source_id), str(target_sink)])

subprocess.run(['pactl', 'set-default-sink', str(target_sink)])