I had never heard of mds but tried it last night and again this morning. whether I try to download the last public beta or development beta I get Busy, please wait....
Yeah. You really do have to wait. The downloads are huge. How long depends on your internet speed.
Frankly I'm more interested in it for older systems, not big sur betas. I get those through my developer account anyway.
I used it to get high sierra yesterday and it worked for me.
Anyway you can check download progress by looking in
~/Library/Application Support/com.twocanoes.macdeploystick/cache (the default temporary folder)
There will be several folders in there but only one of them will be the one it downloads to, so you need to explore the folders a bit to find the relevant one. In the case of big sur it probably will be the last one (unless a point release is made for an older system - after the latest big sur beta release).
It is a good idea to clear this folder after it is finished too.
The folder won't exist until you start a download but there is a button you can press to clear it called "Clear Files":
Just click on the "General" and you will see all this.:
You can also use this to specify another temporary folder instead of ~/Library/Application Support/com.twocanoes.macdeploystick/cache if you wish.