clamav-daemon doesn't create /var/run/clamd.ctl

I installed clamav-daemon on Debian 11 and when I try to start it, it doesn't create the LocalSocket /var/run/clamd.ctl.

LocalSocket in my /etc/clamav/clamd.conf:

LocalSocket /var/run/clamav/clamd.ctl

systemctl status clamav-daemon.service brings:

● clamav-daemon.service - Clam AntiVirus userspace daemon
     Loaded: loaded (/lib/systemd/system/clamav-daemon.service; enabled; vendor preset: enabled)
    Drop-In: /etc/systemd/system/clamav-daemon.service.d
             └─extend.conf, override.conf
     Active: active (running) since Fri 2023-02-17 15:55:18 CET; 34min ago
       Docs: man:clamd(8)
             man:clamd.conf(5)
             https://docs.clamav.net/
    Process: 37394 ExecStartPre=/bin/mkdir -p /run/clamav (code=exited, status=0/SUCCESS)
    Process: 37395 ExecStartPre=/bin/chown clamav /run/clamav (code=exited, status=0/SUCCESS)    Main PID: 37396 (clamd)
      Tasks: 1 (limit: 1129)
     Memory: 489.8M
        CPU: 52.996s
     CGroup: /system.slice/clamav-daemon.service
             └─37396 /usr/sbin/clamd --foreground=true

Feb 17 15:55:18 cc700x-irmler systemd[1]: clamav-daemon.service: Consumed 11.193s CPU time. Feb 17 15:55:18 cc700x-irmler systemd[1]: Starting Clam AntiVirus userspace daemon... Feb 17 15:55:18 cc700x-irmler systemd[1]: Started Clam AntiVirus userspace daemon.

So, it seems everything to be fine. But: systemctl status clamav-daemon.socket brings:

Unit clamav-daemon.socket could not be found.

/var/log/clamav/clamav.log brings (when starting):

Fri Feb 17 15:55:19 2023 -> +++ Started at Fri Feb 17 15:55:19 2023
Fri Feb 17 15:55:19 2023 -> Received 0 file descriptor(s) from
systemd. Fri Feb 17 15:55:19 2023 -> clamd daemon 0.103.7 (OS:
linux-gnu, ARCH: x86_64, CPU: x86_64) Fri Feb 17 15:55:19 2023 -> Log
file size limited to 4294967295 bytes. Fri Feb 17 15:55:19 2023 ->
Reading databases from /var/lib/clamav Fri Feb 17 15:55:19 2023 -> Not
loading PUA signatures. Fri Feb 17 15:55:19 2023 -> Bytecode: Security
mode set to "TrustSigned". Fri Feb 17 16:08:12 2023 -> Loaded 8652992
signatures.

/var/log/clamav/clamav-milter.log brings (as the /var/run/clamav/clamd.ctl is missing):

Fri Feb 17 16:27:05 2023 -> WARNING: No clamd server appears to be
available Fri Feb 17 16:28:05 2023 -> WARNING: No clamd server appears
to be available Fri Feb 17 16:29:04 2023 -> WARNING: No clamd server
appears to be available Fri Feb 17 16:30:03 2023 -> WARNING: No clamd
server appears to be available Fri Feb 17 16:31:02 2023 -> WARNING: No
clamd server appears to be available Fri Feb 17 16:32:01 2023 ->
WARNING: No clamd server appears to be available

The permissions for /var/run/ is set for the user "clamav" and group "root". clamav is also the user who runs the process:

ps aux | grep clamav

clamav       500  0.0  0.0  58248   704 ?        Ss   14:22   0:00
/usr/bin/freshclam -d --foreground=true clamav     31064  0.0  0.0
349480    52 ?        Ssl  14:55   0:00 /usr/sbin/clamav-milter
--config-file=/etc/clama         v/clamav-milter.conf clamav     37396  2.2 42.5 1395520 425952 ?      Ds   15:55   0:55 /usr/sbin/clamd --foreground=true root       38870  0.0  0.0   6244   700 pts/1    S+   16:36   0:00 grep clamav

I tried already to purge/install and also --reinstall clamav and clamav-daemon and I also tried a dpkg-reconfigure on clamav-daemon. And I also tried a clean reboot. Nothing changed the situation.

I have no idea what else I could try. Has anyone an idea? Thanks a lot!