screen time doesn't block twitter

Blocking websites on screen time prevent you from accessing it through Safari browser only, which means it will not work on other browsers like Google Chrome, Mozilla Firefox. As for the Twitter app from the App Store, it is possible to just set an app limit.

To learn more: Set time limits for apps and websites in Screen Time on Mac - Apple Support

Head over to Settings > Screen Time > Content & Privacy > Content Restrictions > Set access web content to Limit Adult Websites > then click Customize > Add twitter.com to the restricted section

There is another way of doing this, but it is not so recommended unless you want to permanently (still revertible) apply this.

The way of doing this is to add twitter.com into the host file.

From the Finder's Go menu select Go to Folder. Enter /private/etc/ in the field and click on the Go button. If a hosts file is present you will see it listed and can edit it per your instructions. If one is not present then use any editor to create a file and save it as hosts with no extension.

You can use TextEdit to edit or create the file. You can also edit it using the Terminal application in the Utilities folder by entering the command, pico, at the prompt and pressing RETURN. Pico is a simple editor but will do the job. If you find it gives an error then try, sudo pico, instead. You will be prompted for your admin password that is not echoed to the screen.

Note: this will prevent any connection from your machine to the listed domains and ip addresses