So this question is probably a result of me not completely understanding the inner workings of Wordpress - especially the home variable.
So here is what I did, and after that I will ask my question.
I did set up a Wordpress on localhost (with a remote database). Then I set up a fileserver for everything (except my .php files) and added it via the cdn-enabler. Now I uploaded my Webiste to AWS and exposed it to the world via an API-gateway, while still using the old database. The website does work well now, even if I shut down my localhost server.
Since my hyperlinks still point to localhost (eg. /about_me would point to localhost/wordpress/about_me), I changed the home in wp-config to "myurl/stage". Now if an go to "myurl/stage/about_me" I will see the about_me page just fine, but as soon as I go to "myurl/stage/index.php" I will get a timeout.
The error persists, either if I only set home, or if I set home and siteurl. If I only change the siteurl the cdn-enabler will stop working, but I can access "myurl/stage/index.php", also all my hyperlinks will point to index.php, e.g: "myurl/stage/index.php/about_me".
Does anyone have a idea what happened here? Can you give me a better insight in how exactly home and siteurl behave?
ps.: Maybe its important to note, that if I set home to "myurl" instead of "myurl/stage" I can access "myurl/stage/index.php". Sadly, if I do this all hyperlinks are broken again. Example: "myurl/about_me"