bluez-alsa-utils (which provides a virtual sound card for playback and capture via bluez bluetooth mediation).

It seems that it does not provide any "virtual sound card".

What it does provide is a sort "virtual PCM device" named "bluealsa"
_https://github.com/arkq/bluez-alsa

aplay -D bluealsa test.wav 

alsamixer -D bluealsa 

 $ bluealsa-aplay -l
**** List of PLAYBACK Bluetooth Devices ****
hci0: EC:66:D1:BF:02:05 [Godess of Wisdom], trusted audio-headphones
  A2DP (SBC): S16_LE 2 channels 48000 Hz
**** List of CAPTURE Bluetooth Devices **** 

It can be configured as default playback device, e.g. ~/.asoundrc.

The question is how to configure a dmix for it.

EDIT:

A very simple ALSA config for Bluetooth Headphones:

$ cat ~/.asoundrc
# -------------------------------------------
#		Bluetooth Headphones
#
#	Configuration for default audio device
#--------------------------------------------

# Perform plug device
pcm.!default
{
	type	plug
	slave.pcm	"bluealsa"
	hint.description	"Default device"
}

$ apt-file find /usr/bin/bluealsa
bluez-alsa-utils: /usr/bin/bluealsa       
bluez-alsa-utils: /usr/bin/bluealsa-aplay

fuser -av $(find /dev/snd -type c 2>/dev/null)

For example:

➤ fuser -av $(find /dev/snd -type c 2>/dev/null)
                     USER        PID ACCESS COMMAND
/dev/snd/controlC0:  igor       2235 F.... mate-settings-d
                     igor       2326 F.... mate-volume-con
/dev/snd/pcmC0D0c:
/dev/snd/pcmC0D0p:   igor       3201 F...m firefox-esr
/dev/snd/seq:
/dev/snd/timer:      igor       3201 f.... firefox-esr

And the output of

inxi -A

sudo apt install inxi

inxi: everything you need to know about your computer
_https://easylinuxtipsproject.blogspot.com/p/inxi.html

# mkdir -p /etc/alsa/conf.d

if it doesn't exist.

in fact, if you look into /usr/share/alsa/alsa.conf which is the main configuration file for alsa, you will see that it looks for configuration files in many places. I suggested /etc/alsa/conf.d/ because that is commonly used by many packages and especially bluez-alsa-utils (which provides a virtual sound card for playback and capture via bluez bluetooth mediation).

Some people prefer using ~/.asoundrc instead, since that is written/editable by the non-root end user. However it will also only be used by that non-root end user and not shared among all users.

➤ apt-file find /etc/alsa/conf.d
...
libasound2-plugins: /etc/alsa/conf.d/10-rate-lav.conf
libasound2-plugins: /etc/alsa/conf.d/10-samplerate.conf
libasound2-plugins: /etc/alsa/conf.d/10-speexrate.conf
libasound2-plugins: /etc/alsa/conf.d/50-arcam-av-ctl.conf
libasound2-plugins: /etc/alsa/conf.d/50-jack.conf
libasound2-plugins: /etc/alsa/conf.d/50-oss.conf
libasound2-plugins: /etc/alsa/conf.d/50-pulseaudio.conf
libasound2-plugins: /etc/alsa/conf.d/60-a52-encoder.conf
libasound2-plugins: /etc/alsa/conf.d/60-speex.conf
libasound2-plugins: /etc/alsa/conf.d/60-upmix.conf
libasound2-plugins: /etc/alsa/conf.d/60-vdownmix.conf
libasound2-plugins: /etc/alsa/conf.d/98-usb-stream.conf
libasound2-plugins: /etc/alsa/conf.d/99-pulseaudio-default.conf.example
...

See also:
_https://www.commandlinux.com/man-page/man1/apt-file.1.html

Post the output of aplay -l Let's see how many audio devices you have and what they are.