Hi @Mathias,
Thanks for reaching out.
I have checked the {{dc:url:segment}} in my local environment and found it working properly while showing the value from the URL or while using it in the condition. I would suggest you add the {{dc:url:segment}} into a text element and check if that is showing the correct value or not. If not, you can also test that by creating a new page and setting that as the child page of another page, and then add the code into the text element and check if that code is showing the parent page as a result of it. If not, there might be some different reasons behind your issue. I would like to suggest troubleshooting the following common issue to help us to recognize the reason.
1.Theme Related Issue
2.Plugin Conflict
3.Theme Update related issue ** if you have activated it
4.Child Theme Related issue
5.CSS/JS Customization
6.Disabling Cache
7.Permalink
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Thanks