In the documentation for adding a guest data extension it specifies that the data extension name must be ext.
Therefore the endpoint needs to be:
For the endpoint, use
extext shows up in both profile and basic segments UI
extExt shows up in profile but not basic segments UI
ext results in a 404 response
Once the data extension is setup like this, then you can query the field in the segmentation UI or search of the fields in the search bar.
One thing to note is the data model being used here in segmentation is updated every 24 hours, so after you add your new data extension you will need to wait 24 hours until you can see the field available in the UI for segmentation.