I solved this by adding the following lines into my Docker file:

# "xdebug-2.9.0" for PHP<=7.4 — "xdebug" (3) for PHP>=8
ARG XDEBUG_VERSION="xdebug-2.9.0"

FROM php:7.0-apache

RUN a2enmod rewrite

RUN docker-php-ext-install pdo pdo_mysql

RUN yes | pecl install ${XDEBUG_VERSION} \
    && echo "zend_extension=$(find /usr/local/lib/php/extensions/ -name xdebug.so)" > /usr/local/etc/php/conf.d/xdebug.ini \
    && echo "xdebug.remote_enable=on" >> /usr/local/etc/php/conf.d/xdebug.ini \
    && echo "xdebug.remote_autostart=off" >> /usr/local/etc/php/conf.d/xdebug.ini


COPY php.ini /usr/local/etc/php/
COPY . /var/www/html/

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}

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

Works for me on Ubuntu 20.04.

Add to you project's docker-compose.yml

(https://github.com/docker/for-linux/issues/264#issuecomment-772844305)

services:
  your_php_service_name:
    extra_hosts:
      - host.docker.internal:host-gateway

In your CLI run export XDEBUG_TRIGGER=1 && export PHP_IDE_CONFIG="serverName=host.docker.internal" to start xdebug with the request.

Thanks @LazyOne for his comment to the question with the solution.