Firstly, this isn't specific to Quarto as it doesn't run in the shinylive editor either. I suspect it's related to how {vroom} opens URLs - it has a dependency on {curl} which isn't available in webR and it might well rely on that to download files via a URL. I can open a file fine using the same method but read.table() instead of vroom::vroom() (which I think uses download.file() instead of {curl}), so if you can convert your data to a file format that read.table() can handle, it should work. I'm a bit confused why you need reactiveFileReader() in the first place though - it's normally used when a file is being frequently updated.
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.