I’m using Brave version 0.22.669 on macOS High Sierra version 10.13.4.
Let’s consider the following url:
In Chrome, if I want to highlight the part of the url address above that is in blue, then, using the mouse, I click and place the cursor right after www.bbc.com and then drag the mouse pointer downwards slightly to the right to highlight everything that follows to the right of the cursor. Everything up to the end of the line will get highlighted. Similarly, if you want to highlight everything to the left of the cursor up to the beginning of the url address, one has to drag the mouse pointer downwards and then slightly to the left (instead of the right).
Dragging downwards doesn’t do anything in Brave. Instead, one has to drag the mouse pointer all the way to the end of the line to highlight it.