The issue turned out to be the header size limit in nginx.
https://ww.wp.xz.cn/support/topic/502-bad-gateway-36/
These nginx directives fixed it for me:
proxy_buffer_size 128k;
proxy_buffers 4 256k;
proxy_busy_buffers_size 256k;
Ok, apparently the index.php needs to be there. I missunderstood the provided post about the permalinks issue.
Both article links are working now with the following permalink settings:
Custom Structure: /index.php/%category%/%postname%/
Category Base: /category
Tag Base: /tag
That still leaves the question about the URL on this’n.
http://blog.stephenrushing.com/index.php/wordpress/6/