Windows 11 - Shift+Left Click to open a new instance of app

Demotis, the issue is not in lack of support of this feature - it is still there. What is not the same as it used to be in Windows 10 is a simulation of middle-button mouse clicks by using the combination of LeftShiftKey + LeftMouseButton. If you were using a regular mouse, then the middle-button click on the program's icon on the taskbar would open a new instance/window for you as usual. 
  
It is not very difficult to fix this missing part...

Create a text file with an extension .ahk with the following content:

<+LButton::MButton

Download and install https://www.autohotkey.com/, and use its utility Convert .ahk to .exe to create a very small ~1.16 MB .exe program (for those who don't want to make this on their own, I am attaching both .ahk and .exe files). Then move this program or a shortcut to this program to your Startup folder (to open that folder press Win+R and enter shell:Common Startup).

If you don't want to restart your Windows yet, execute this program manually for immediate use.

Good luck!