How to configure multiple sites with same URL on Nginx - nginx

Question

I am trying to have 2 websites running on the same adress,
I want everything request on my.website.com/test_slim and every my.website.com/test_slim/anything/following to be directed on /var/www/html/test_slim/src/public/index.php.
I want everything else (my.website.com/, my.website.com/foo, my.website.com/bar/baz ...) to be served as normal PHP files in /var/www/html/whatever/file/according/to/url/index.php
Fow now, this are my server configurations :
In /etc/nginx/site-enabled/my-default
server {
listen 80 default_server;
listen [::]:80 default_server;
root /var/www/html;
index index.php index.html index.htm index.nginx-debian.html;
server_name _;
location / {
try_files $uri $uri/ =404;
}
location ~ \.php$ {
fastcgi_split_path_info ^(.+\.php)(/.+)$;
fastcgi_pass unix:/run/php/php7.2-fpm.sock;
fastcgi_index index.php;
include fastcgi.conf;
}
}
In /etc/nginx/sites-enabled/test_slim
server {
listen 80;
server_name _;
index index.php;
error_log /var/www/html/test_slim/error.log;
access_log /var/www/html/test_slim/access.log;
root /var/www/html/test_slim/src/public;
location /test_slim/ {
try_files $uri /index.php$is_args$args;
}
location ~ \.php {
try_files $uri =404;
fastcgi_split_path_info ^(.+\.php)(/.+)$;
include fastcgi.conf;
fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
fastcgi_param SCRIPT_NAME $fastcgi_script_name;
fastcgi_index index.php;
fastcgi_pass unix:/run/php/php7.2-fpm.sock;
}
}
But what I actually get is :
Request on localhost/ execute /var/www/html/index.html as wanted.
Request on localhost/toto execute /var/www/html/toto/index.html as wanted.
Request on localhost/test_slim downloads the /var/www/html/test_slim/src/public/index.pxp
Request on localhost/test_slim/hello returns us a Nginx error page (404 if hello folder doesn't exist, 403 if it does).
Request on localhost/test_slim/src/public/ exectute the /var/www/html/test_slim/src/public/index.php file.