I ended up going the nuclear option and just doing a fresh windows install since honestly there appears to have been funky things happening with more than just Brave. So far so good, but I will report back if that changes…
Edit 20240719 - @Mattches for awareness; the above was my solution for any who come after me with a similar situation. I think in my case there was something up with my install of Windows 10 – what I don’t know. I nuked it and did a fresh, brand spanky new Windows 11 install and have had no issues since. Marking this as my solution.