And finally I found a crappy solution :
Inspired by the rewriter provided with the official prestashop docker image, I modified my docker's apache vhost and added the following line :
php_value auto_prepend_file /docker_prepend.php
From now, each webpage called from the prestashop hosted inside our docker dev environment is now preprended with these few php lines :
<?php
$pdo_dsn = sprintf('mysql:host=%s;dbname=%s', getenv('DB_SERVER'), getenv('MYSQL_DATABASE'));
$DBHandler = new PDO($pdo_dsn, getenv('DB_USER_FRONT'), getenv('DB_PASSWD'));
$DBStatement = $DBHandler->prepare("UPDATE `ps_shop_url` SET `domain` = :domain, `domain_ssl` = :domain WHERE `id_shop` = :shop_id AND `domain` != :domain;");
$DBStatement->execute([
'domain' => $_SERVER['HTTP_HOST'],
'shop_id' => getenv('SHOP_ID'),
]);
If the current request comes from an http_host which is not the same as the domain used by the targetted shop_id, the domain is rewritten just before prestashop is initiated.
That's not perfect, but it definitely works and allows all of us to work on our local environments, sharing the same database, reaching any local server without taking care of the hostname.
Edit : Oh and of course, this setup, as the prestashop codebase are now shared and deployed by using git.