I worked for a short time on SearchGPT, and I can tell you OpenAI does respect robots.txt , at least when I was there and does now. They are also careful to shard per domain and only crawl each domain at a small rate (~1 qps) as to not ddos the site. OpenAI also uses User Agent strings to identify itself: https://platform.openai.com/docs/bots
They have dedicated user agents for search crawling, when a user directly asks about a site and for training data.