If you got a HTTP 500 error, there is something not working within your HTTP Server (aka internal server error). You should see something more in your server log files.
Actually your HTTP server version is completely out of date, try to upgrade to Apache 2.4
Also, you could try if your web server is delivering content at all by placing a minimal index.html file into the document root and a minimal index.php file to check for working PHP. I.e. the follwing index.php file will give you a lot of useful information about your web server/PHP combination:
Seems that your webserver is not able to access your files. Might be about permissions. Are you able to run any other website succesfully on this server, i.e. the static index.html file which I mentioned above?
However, most probably this is not related to Kirby. You should try to get a working webserver with PHP first, and if you can successfully launch the index.php with phpinfo, you are ready for the next step.
Personal remark: From my own experience, these kind of devices, be it Synology or QNAP or anything else, usually have a completly quirky and obstructed implementation of a webserver - most probably because there are serving a kind of management interface which is also more or less quirky. To be able to serve a state of the art webserver, maybe you are better off by purchasing a low cost device like a Raspberry Pi where you can work with a standard linux server.
On the Synology DS 214 Play I got it running. Initially I got confused, because Synology offers the possibility to have Userwebsites. Unfortunately the Userwebsites only support PHP 5.6, I do not understand why Synology keeps this confusing Possibility in their toolset?!?
After figuring this out, the installation was pretty easy and it works, also with more than one site.
On the Raspberry Pi installation of PHP 7.4 and Apache2 was pretty straight forward. I struggled a while with setting up virtual hosts as I did not want to change the hosts file on every device I am using… With PiHole I found the perfect solution. It allows to set up local DNS
Additionally I have an Addblocker at the same time for all devices within my local network.
So thanks again for replying and getting me on the right track!
Thats perfect, glad you figured it out! I am using basically the same solution which enables me to just view any new website on the Pi from any device in my household without any further configuration.
In fact, the Pi-hole software contains a DNS Resolver, something which one could install separately if Pi-hole is not the favoured solution. The router in a home network usually already contains a DNS resolver as well - but without an interface to configure it.