My config: Brave 1.77.101 with Chrome 135.0.7049.115, Windows 10 Home x64 22H2
In Firefox and Edge, I can drag the padlock icon at the left side of the address bar to the desktop to create a URL shortcut. In Brave, there is nothing I can drag to the desktop or into a folder to create a URL shortcut.
With Brave, I have to click on the Share icon at the right side of the address bar, select Copy Link, and then go through the process of creating a new shortcut (e.g., right-click on the desktop, New, Shortcut, copy into the Target field, name the shortcut, Finish the shortcut), and finally I have a URL shortcut to the web page.
In a forum post, someone said to use Settings → More tools → Create shortcut. That doesn’t exist in my Brave. Even if it did, that is a lot more mouse clicking than a simple drag-n-drop that Firefox and Edge have.
UPDATE
I just started to test dragging all toolbar icons from Brave to the desktop. I discovered dragging the “View site information” icon (looks like 2 round-headed pushpins facing in opposite directions) will let me drag-drop to create a shortcut.