I want to add a new extension, but I don't have the "Get extension" Option. Please check above screenshot.
Have a look at the blue box: your instance is running in composer mode, so you have to use composer to install extensions.
Please use composer require
to add new extensions see https://docs.typo3.org/m/typo3/guide-installation/10.4/en-us/ExtensionInstallation/Index.html#install-extension-with-composer