binfmt-support cannot start at boot time because /var is not mounted

[Dmitry Katsubo <dma_k@mail.ru>]

Dear Debian users,

I am stuck with the following problem which I failed to debug on my Debian 10.3.

In my setup I have /var as mounted volume:

=== /etc/fatab ===
UUID=83a3cb60-3334-4d11-9fdf-70b8e8703167    /var    btrfs    noatime,nodev,nosuid,subvol=var
=== end ===

Unfortunately sometimes I notice that binfmt-support is tried to be started "before" /var is mounted. Once I login and restart the service (I don't mount and/or repair anything), it starts just fine.

=== console ===
root@debian:~ # systemctl status binfmt-support
* binfmt-support.service - Enable support for additional executable binary formats
   Loaded: loaded (/lib/systemd/system/binfmt-support.service; enabled; vendor preset: enabled)
   Active: failed (Result: exit-code) since Sun 2020-05-10 21:54:27 CEST; 10h ago
     Docs: man:update-binfmts(8)
  Process: 353 ExecStart=/usr/sbin/update-binfmts --enable (code=exited, status=2)
 Main PID: 353 (code=exited, status=2)

May 10 21:54:27 debian update-binfmts[353]: update-binfmts: unable to open /var/lib/binfmts: No such file or directory

root@debian:~ # ll /var/lib/binfmts
total 16
drwxr-xr-x 1 root  root  50 Mar 17 23:46 .
drwxr-xr-x 1 root  root 988 Mar  2 01:57 ..
-rw-r--r-- 1 root  root  49 Apr 14  2019 jar
-rw-r--r-- 1 root  root  59 Mar 17 23:46 python3.7

root@debian:~ # systemctl start binfmt-support
root@debian:~ # systemctl status binfmt-support
* binfmt-support.service - Enable support for additional executable binary formats
   Loaded: loaded (/lib/systemd/system/binfmt-support.service; enabled; vendor preset: enabled)
   Active: active (exited) since Mon 2020-05-11 09:01:04 CEST; 4s ago
     Docs: man:update-binfmts(8)
  Process: 9683 ExecStart=/usr/sbin/update-binfmts --enable (code=exited, status=0/SUCCESS)
 Main PID: 9683 (code=exited, status=0/SUCCESS)

May 11 09:01:04 debian systemd[1]: Starting Enable support for additional executable binary formats...
May 11 09:01:04 debian systemd[1]: Started Enable support for additional executable binary formats.

root@debian:~ # dpkg -l | grep -i systemd
ii  systemd   241-7~deb10u3     amd64   system and service manager
...
=== end ===

One time the system was started with even more units failed because of inaccessible /var. There is nothing special in these units, and I haven't modified any *.service files. In other words the
problem is floating, as number of failed unit varies from boot to boot.

The difficulty is that I don't know how to debug system start / systemd at such early stage of system boot.

Any help is appreciated.

-- 
With best regards,
Dmitry