fastcgi does not work

I am unable to get this to work via fastcgi with a simple php-fpm container. Here’s my docker-compose.yml file:

version: "3"

services:
  proxy:
    image: jwilder/nginx-proxy
    ports:
      - "80:80"
    volumes:
      - /var/run/docker.sock:/tmp/docker.sock:ro
    environment:
      - DEFAULT_HOST=test.local

  fpm:
    image: php:fpm
    environment:
      - VIRTUAL_HOST=test.local
      - VIRTUAL_PROTO=fastcgi

I then drop in a simple index.php file by running:

 docker container exec -it web_fpm_1 /bin/bash -c 'echo "<?php phpinfo(); ?>" > /var/www/html/index.php'

(It puts web_ in front because this project is in a directory named web/.)

I also modify my hosts file to point test.local to 127.0.0.1, so I can test it. However, every attempt to browse to test.local results in a blank white page.

The logs for the web_fpm_1 container show that nothing gets sent except a 200 response:

[06-Jul-2020 15:40:39] NOTICE: fpm is running, pid 1
[06-Jul-2020 15:40:39] NOTICE: ready to handle connections
172.19.0.3 -  06/Jul/2020:15:41:02 +0000 "- " 200
172.19.0.3 -  06/Jul/2020:15:41:03 +0000 "- " 200

What am I doing wrong?

[tkw1536]

Based on the example by @flowl I have implemented https://github.com/tkw1536/nginx-proxy-fpm-workaround. This solution does not require manually intervening in the nginx-proxy container. It additionally serves non-php files statically.

[flowl]

@tkw1536 in the config is no try_files $uri $uri/ /index.php and in fastcgi_params or the default.conf there is no fastcgi_param SCRIPT_FILENAME $request_filename;