How to get time synced outputs (different timezones on servers)

.INIT.          16 u

That's not fine. You either queried the state to soon, or your ntpd can't connect to those servers at all. When it is synced, it should display IP addresses or host names in the refid column, and values like 2 or 3 in the st column.

The output of a working ntpd should look like this:

iserv ~ # ntpq -p     
     remote           refid      st t when poll reach   delay   offset  jitter
==============================================================================
*char-ntp-pool.c .shm0.           1 u  162 1024  377   33.332   -5.160   1.225
+node3.mneisen.o 192.53.103.108   2 u  145 1024  377   30.391   -0.756   1.122
+38.101.77.21    64.113.32.5      2 u 1673 1024  336  184.925   20.728  18.911
-ntp0.sanctioned 131.188.3.221    2 u  563 1024  377   30.445  -50.495  18.027

Most programs read the timezone settings once at start-up and won't expect them to change while the program is running.

So, you'll need to restart any programs with incorrect timezone:

root@debian:~: systemctl restart rsyslog

root@debian:~: systemctl restart apache2

You should also update the initramfs file, so that the correct timezone will be set as early as possible in the boot process:

root@debian:~: update-initramfs -u

It looks like Apache might be using the UTC timezone. That might be intentional: it is possible to use the TZ environment variable to set a specific timezone to specific programs, if e.g. some sort of log post-processing requires the logs of some services to be in UTC time. This might be set in /etc/apache2/envvars.

Your syslog daemon might be using the US Eastern timezone. That is a common "factory default" for US-centric software, and is probably what your timezone was set to before you changed it to Tehran.

(I would have expected Debian to use UTC as the factory default instead, but perhaps there are some historical backwards compatibility reasons why not.)