Your answer was beneficial and helped me to find the problem. However, it is not correct, as shinylive is working with both {vroom} and {readr}.
The problem was my URL: I used as file path 'https://github.com/petzi53/…' instead of the correct URL 'https://raw.githubusercontent.com/petzi53/…'.
And now comes the peculiar thing: The Shiny app worked using {vroom} with my 'github.com' URL, but shinylive did not. There is a second anomaly: I emphasized my because it worked with my (wrong) URL but not with yours.
But whatever the reason for the second oddity, the main problem was my wrong URL.
I apologize for my mistake and thank you for your patience.
As the problem is solved, I will close this post.
PS.: You are right to be confused with my using of reactiveFileReader(). It was a desperate move after trying different options for several hours. I thought that the problem had to do with reactivity.