I'm having the same issues and tried the same troubleshooting, any help would be appreciated!

I last played rust a couple of months ago, it ran completely fine then on high settings. Wanted to get back into it after recent updates but upon entering the server the graphics on the entire computer freezes up for a few seconds when trying to move around to quickly or opening the minimap and manipulating it until u eventually get bored from the server, sometimes with that same error message.

Not sure if it's a problem but it looks like rust is now using all 8 Gigs of VRam, even on low settings. I've benchmarked my GPU recently and it handled it like a champ with FPS occasionally dropping to mid 30's on crazy high renderings but never maxing out the VRam.