Solution
@Nic Brough -Adaptavist- pointed out, that the proxy setup should come after installation of JIRA.
I had some issues with this way back in my beginning with JIRA so I did not use this approach at first.
Now I ended up in doing so and discovered no issues at all. It works all fine now!
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I have the following environemnt:
- Debian 9 Stretch
- PostgreSQL 9.6 (from Debian repository)
- nginx 1.12.1 (from nginx.org repository)
- TAR.GZ file for JIRA Software server 7.4.1
I have tried the following installation documents in the following order:
- https://confluence.atlassian.com/adminjiraserver074/installing-jira-applications-on-linux-from-archive-file-881683171.html
I did not start JIRA in this step! Need to setup proxy first. - https://confluence.atlassian.com/jirakb/integrating-jira-with-nginx-426115340.html
I did not start JIRA in this step! There are missing parameters for the connectors. - https://confluence.atlassian.com/adminjiraserver074/running-jira-applications-over-ssl-or-https-881684081.html
I did not start JIRA in this step! Updated the missing SSL parameters for the connectors.
I tried to start JIRA:
sudo -u jira /jira/bin/start-jira.sh -fg
I received a bunch of warnings and errors and the process got finally crashed.
The full error log can be reviewed here: https://pastebin.com/WDz0n2tw
I would like to point out some parts of the log but I hit some database field character limit, Atlassian Community throws some error without any highlight. This is my 20th try to submitting this issue. 
Here is my server.xml:
<?xml version="1.0" encoding="utf-8"?>
<Server port="5900" shutdown="SHUTDOWN">
<Listener className="org.apache.catalina.startup.VersionLoggerListener" />
<Listener className="org.apache.catalina.core.AprLifecycleListener" SSLEngine="on" />
<Listener className="org.apache.catalina.core.JreMemoryLeakPreventionListener" />
<Listener className="org.apache.catalina.mbeans.GlobalResourcesLifecycleListener" />
<Listener className="org.apache.catalina.core.ThreadLocalLeakPreventionListener" />
<Service name="Catalina">
<!-- Nginx Proxy Connector -->
<Connector port="5901"
maxThreads="150"
minSpareThreads="25"
connectionTimeout="20000"
enableLookups="false"
maxHttpHeaderSize="8192"
protocol="org.apache.coyote.http11.Http11Protocol"
useBodyEncodingForURI="true"
redirectPort="5902"
acceptCount="100"
disableUploadTimeout="true"
bindOnInit="false"
proxyName="jira.example.com" proxyPort="80"/>
<!-- Nginx Proxy Connector with https -->
<Connector port="5902"
maxThreads="150"
minSpareThreads="25"
connectionTimeout="20000"
enableLookups="false"
maxHttpHeaderSize="8192"
protocol="org.apache.coyote.http11.Http11Protocol"
useBodyEncodingForURI="true"
acceptCount="100"
disableUploadTimeout="true"
bindOnInit="false"
proxyName="code.soeren-kornetzki.de" proxyPort="443"
SSLEnabled="true" scheme="https" secure="true"
sslEnabledProtocol="TLSv1.2" clientAuth="false" sslProtocol="TLSv1.2"
keyAlias="mycert" keystoreType="JKS" keystoreFile="/jira/keystore" keystorePass="changeit"/>
<Engine name="Catalina" defaultHost="localhost">
<Host name="localhost" appBase="webapps" unpackWARs="true" autoDeploy="true">
<Context path="/jira" docBase="${catalina.home}/atlassian-jira" reloadable="false" useHttpOnly="true">
<Resource name="UserTransaction" auth="Container" type="javax.transaction.UserTransactiofactory="org.objectweb.jotm.UserTransactionFactory" jotm.timeout="60"/>
<Manager pathname=""/>
<JarScanner scanManifest="false"/>
</Context>
</Host>
<Valve className="org.apache.catalina.valves.AccessLogValve" pattern="%a %{jira.request.id}r %{jira.request.username}r %t "%m %U%q %H" %s %b %D "%{Referer}i" "%{User-Agent}i" "%{jira.request.assession.id}r""/>
</Engine>
</Service>
</Server>
How to install JIRA Software server 7.4.1 for a nginx proxy with SSL setup?
PS: Pasting in the Code block still removes all the indention! 
To Atlassian: Stop cutting off your support and force payed users to use Atlassian Community while it is beta quality at tops. So many bugs which - for me - makes it unusable.
Edit2: After changing the protocol to "org.apache.coyote.http11.Http11NioProtocol" I got the other issue "Not implemented for JIRA bootstrap time": https://pastebin.com/4x9Ke3AG