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Your LimeSurvey version: 5.6.1+230123
Own server or LimeSurvey hosting: own server
Survey theme/template: Fruity
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My survey has questions...

My survey's questions are in groups...

But the "Structure" interface is empty.

Is my installation broken? 
Survey (lss) and sample group (lsg) attached

Is it the same with all surveys?

Try updating to the latest version.

It is not the same with all surveys, and I have updated to the latest version.

But it is the same with all recent surveys. I have two which still show the group/question structure, and they were made about a month ago. However, I also have one from December of last year that does not. And if I create one from scratch in LimeSurvey (most of my surveys are uploaded TSV files), it does not have the group/question structure.

I've tried clearing the cache (Global Settings -> General -> Clear asset cache), but all that seems to do is increment the "Clear assets cache" number, which is somewhat puzzling.  

Your survey works for me - see below.

I assume that you are not using a custom admin theme.

If not, I'm afraid I don't have any suggestions.