Just starting to use Parallels Tools V5.01 on Big Sur 11.6 on an M-1 Mac and have found that Screenshot Page doesn't work. I've tried both pasting a link to it, as well as dragging the URL from the Safari address bar. The screen darkens and the warning message not to to scroll appears, but no output is made. The output is supposed to go to the desktop.
I have Catalina v10.15.7 and Parallels Tools v5.01. I just used the Screenshot Page for the first time today and gave it the permissions it needed in System Preferences. I experienced the exact same thing as you described DHK. I also tried both dragging and pasting different urls, several times, with both Safari and Firefox. As well, I quit/reopen Parallels Tools and tried changing the output location to my Downloads folder to see if that would help. Still no output.
@MarioH2 Interestingly enough it worked fine on another Big Sur Mac non-M1. I'm going to check the permissions on the iMac that it fails on.
I updated Parallels to the latest version, 17. After updating it, I went to Parallels Tools again and it was requiring the license. I reinstalled the license and now it is working correctly.