TYPO3 12 not working after extension install

While making some of my extensions compatible to TYPO3 v12, I stumbled across the problem, that the whole TYPO3 website did not work anymore (frontend/backend) after the extension has been installed. Obviously there was no error message in the logs available, and it took me some time to figure out, why the website was not working.

With TYPO3 11.5, the legacy constant TYPO3_MODE was deprecated. My extension did still use the old constant, so the code defined('TYPO3_MODE') or die(); resulted in a hard exit of the code in ext_localconf.php. After migrating the code to defined('TYPO3') or die();, TYPO3 worked again.