Most browers should download Sibelius files just fine, including, at time of writing, Edge and Firefox.
However, Chrome seems to think they are dangerous, and prevents the download.
They are not dangerous!
But it is easy to get around this. Once you have attempted to download the file (or files), view your downloads page (ctrl+J,), and click ‘keep dangerous file’ to download it.
Advice accurate as of 21/7/21.