RUN apk add --no-cache $PHPIZE_DEPS \
    && pecl install xdebug-2.9.2 \
    && docker-php-ext-enable xdebug  \

As the name points out the command docker-php-ext-install is meant to install a PHP extension – an .so file. Using PECL is just another way of installing extensions, so, by trying to use docker-php-ext-install after a pecl install you are trying to do twice the same thing.

And as the end of the pecl install points out:

You should add "zend_extension=/usr/local/lib/php/extensions/no-debug-non-zts-20190902/xdebug.so" to php.ini

Which would be what docker-php-ext-enable is meant to do.

So, your working Dockerfile would be:

FROM php:7.4

RUN pecl install xdebug-3.1.5 \
      && docker-php-ext-enable xdebug

This is actually pointed out in the documentation of the php image:

PECL extensions

Some extensions are not provided with the PHP source, but are instead available through PECL. To install a PECL extension, use pecl install to download and compile it, then use docker-php-ext-enable to enable it:

FROM php:7.4-cli
RUN pecl install redis-5.1.1 \
      && pecl install xdebug-2.8.1 \
      && docker-php-ext-enable redis xdebug

^{Source: https://hub.docker.com/_/php}

Xdebug traffic wasn't finding it's way back to my host. When I entered the IP-address of my host machine in xdebug.remote_host, debugging worked but this was not ideal because my IP changes on every reboot. Luckily, Docker provides a way to obtain the host IP via a DNS-entry docker.for.win.localhost.

Edit:
Docker now has a platform-independent DNS-entry host.docker.internal.

I tried to use xdebug.remote_connect_back=1 which just responds to traffic from where it came but it wasn't working. Phpinfo() showed that REMOTE_ADDR was set to localhost. Localhost in this context points to the Docker PHP-container while it should point to our host IP. Important to know with this setting is that xdebug.remote_host in the .ini will be ignored.

From the Xdebug docs:

xdebug.remote_connect_back Type: boolean, Default value: 0, Introduced in Xdebug >= 2.1

If enabled, the xdebug.remote_host setting is ignored and Xdebug will try to connect to the client that made the HTTP request.

Here is the Dockerfile with the xdebug.ini configuration for the PHP Docker container that worked:

FROM php:7.1-fpm
ARG TIMEZONE

MAINTAINER Maxence POUTORD <[email protected]>

RUN apt-get update && apt-get install -y \
    openssl \
    git \
    unzip

# Install Composer
RUN curl -sS https://getcomposer.org/installer | php -- --install-dir=/usr/local/bin --filename=composer
RUN composer --version

# Set timezone
RUN ln -snf /usr/share/zoneinfo/${TIMEZONE} /etc/localtime && echo ${TIMEZONE} > /etc/timezone
RUN printf '[PHP]\ndate.timezone = "%s"\n', ${TIMEZONE} > /usr/local/etc/php/conf.d/tzone.ini
RUN "date"

# Type docker-php-ext-install to see available extensions
RUN docker-php-ext-install pdo pdo_mysql

# install xdebug
RUN pecl install xdebug
RUN docker-php-ext-enable xdebug
RUN echo "zend_extension=/usr/local/lib/php/extensions/no-debug-non-zts-20160303/xdebug.so" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini
RUN echo "error_reporting = E_ALL" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini
RUN echo "display_startup_errors = On" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini
RUN echo "display_errors = On" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini

# relevant to this answer
RUN echo "xdebug.idekey=\"PHPSTORM\"" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini
RUN echo "xdebug.remote_port=9000" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini
RUN echo "xdebug.remote_enable=1" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini
RUN echo "xdebug.remote_autostart=1" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini
RUN echo "xdebug.remote_host=docker.for.win.localhost" >> /usr/local/etc/php/conf.d/docker-php-ext-xdebug.ini

RUN echo 'alias sf="php app/console"' >> ~/.bashrc
RUN echo 'alias sf3="php bin/console"' >> ~/.bashrc

WORKDIR /var/www/free-energy/symfony

Edit:
I was messing around with XDebug quite a bit in this post.
Now I know your XDebug config doesn't have to be as big as I had back then.

xdebug.ini: (in your Docker PHP image).

zend_extension=xdebug.so

[Xdebug]
xdebug.remote_enable=true
xdebug.remote_port=9000
xdebug.remote_host=host.docker.internal