xDebug
Since xDebug v3 is controlled by environment variable and runs only then browser sends the header to enable it.
PHP 7.2 and up includes xDebug 3.X and is much faster.
PHP 7.1 and lower has 2.x and runs xDebug on every request and is untested in Docker Mate.
Browser extension
List matches the extensions on xDebug documentation site, but there are also some alternatives available.
Firefox
Small icon in address bar and settings allow you to set a session-key like
PHPSTORM; Also a shortcut is available.
https://addons.mozilla.org/en-GB/firefox/addon/xdebug-helper-for-firefox/
Chromium
Looks similar to the Firefox Addon
https://chrome.google.com/webstore/detail/xdebug-helper/eadndfjplgieldjbigjakmdgkmoaaaoc
Other
There different ways engage xDebug support from your Browser to your IDE. Please check the documentation from your Editor or IDE.