Wikipedia provides a nice overview of this particular worm and the damage it ultimately caused: https://en.wikipedia.org/wiki/Code_Red_(computer_worm)
It's by no means the only instance of such a worm, but it was one of the most notorious. I was running a webserver on my personal laptop back then, and I recall seeing this request pop up a lot over the summer as various infected webservers tried to attack my little server.
If the Bing Chat search backend had a buffer overflow bug (very unlikely these days), Sydney could exploit it on the server to run arbitrary code in the context of the server. Realistically, while Sydney itself is (probably) not capable enough to send malicious code autonomously, a human could likely guide it into exploiting such a bug. A future GPT-like model trained to use tools may well have enough knowledge of software vulnerabilities and exploits to autonomously exploit such bugs, however.