On my Pixel C tablet I have Brave1.17.75 with Chromium 87.0.4280.88.
I use Brave on many of my laptops and desktop systems. However, it has been most important as my default tablet browser when I installed it 6 months ago. The primary reason for this is that it forces Desktop Site.
Now, I have many web sites that have been “Add to the home screen” aka a shortcut. In the past, when I selected one of these site icons, the site would open in desktop mode.
However, about three months ago this all changed and some sites would open in mobile mode. I have tried and tried to fix this but to no avail. I have tried every “remedy” available on the web short of rooting my tablet. FWIW, the chrome browser appears to have the same problem, open a URL, sellect Desktop site, save as a desktop link, close chrome browser, select the desktop link and … its opened in mobile mode.
Yes, I have gone into settings and select Desktop mode.
Yes, the site had Desktop site selected when I selected Add to Home Screen.
I know this is probably an upstream issue. But, I have had to switch to the Yandex browser for some of my desktop links.
To test:
Go to ubuntuforums.org
With Desktop site select Add to home screen
Exit browser
Click on the desktop link just created.
You should see that the site is in Mobile layout even though the Desktop site option is checked.