Description of the issue:
There are no sites listed at all in history Steps to Reproduce (add as many as necessary): 1. 2. 3.
Brand new installation. I go in history and there is nothing there.
. . . IF you created more than the initial, default Brave Browser user Profile.
Magnifying your 2nd image, you are actually asking about RECENT TABS.
I imagine that list is in some RAM storage for the display.
The list of RECENT TABS might also be in one of the Tabs_0928750860 (string of numbers that represent date and time (I guess), that follow “Tabs_”) files.
The only way to read those files’ contents, is by having them where they are. They are encrypted, and only the Brave Browser’s function(s) can render/reveal their data.
RECENT TABS data might be in a Cache file, but I am not sure, where that would be.
Having written all that, your 2nd image shows the information that you seek - that you could use as search criteria in an Internet search engine’s search field.