No, the permissions don’t get reset. Nothing gets cleared on exit.
It goes like this:
I start my PC → Brave starts in the tray(I use extension for that) → no push notifications pop up from the site X. Nothing! Then I go to the site X and THEN they all start to pop up! As if visiting the site wakes up the browser to it’s normal functionality. Then all is fine until next PC reboot (or manually force-closing the browser). Rinse and repeat.
Even if I set Brave to start with windows (shell:startup shortcut) - same thing - no notification pops up until I manually open the site! And it’s the same for the notifications here, on Brave community - nothing notifies until I open it!