No, I don’t actually have those additional problems the OP was dealing with – I only ran into the auth prompt.
If Seahorse is locked, I get the auth prompt when Brave starts up, but if I decline to unlock it a few times the prompting will stop and the browser loads.
At that point Brave seems to still work just fine, although my Sync settings are effectively disabled. They all appear to be turned off, and if I change them, they just get turned back off again if I close and re-open Settings. I’m guessing the Sync chain key is stored in Seahorse somehow and is inaccessible when it’s locked, but the browser doesn’t have a way of providing feedback here to tell me there’s an issue.
If I close Brave, unlock Seahorse, and then open Brave again – no prompting, and, my Sync settings are back to normal. Same thing if I log out, but log back in using a password, since Seahorse will get unlocked.
I haven’t seen any crashes or any ‘Internet not working’ stuff. Whatever is going on there, I suspect is a separate issue specific to the OP.