Hi there,
Exactly same problem here: Safary is completely unusable after big sur upgrade from cata on a MBP2018. No problems with firefox dev ed, chrome or brave.
I have just reinstalled again as sugested by an apple tech, but no luck...
I also think that there are other problems related to this one: for instance, programs like VSCode does not start inmediately. It seems that they try to stablish a tcp connection but they cannot, so there is a 10 secs time frame, even more, before the application continues loading :S. Really frustrating!
I hope it get solved somehow, but I think even apple care techs do not know how to isolate and handle the problem.
I'm having this problem too on several Macs, but sporadically. I've noticed that when it occurs, that umount appears in the Activity Monitor spiked at 100% cpu. I am unable to kill the process even with force quit or kill -9. After the process eventually crashes, safari goes back to normal.
If anyone else is still experiencing this issue, can you check your activity monitor to see if umount is running?
TLDR; Try disabling Time Machine or removing faulty Time Machine targets.
After working on this for awhile, I think I've figure out what's causing the issue that I'm seeing with umount and Safari. Each time that umount is stuck and Safari is non-responsive, Time Machine was failing to access a disk over the network. I've seen it both with a Synology Time Machine share and a Mac OS Server Time Machine share. Removing the faulty Time Machine target or disabling Time Machine altogether appears to result in the issue no longer happening. I hope that this helps at least some of you.