In online Claude I often use incognito mode precisely because I don't want results to be influenced by what we talked about earlier. It's getting rather annoying to be honest.
I'm switching from Claude Web to Claude Code. Local files give me memory I actually control, unlike Anthropic's implementation. CC doesn't carry state between sessions — you just put whatever project context it needs in a file.
Why not turn it off then?
Keep your user prefs minimal and use project memory instead: create a new project, it will only have access to your user prefs, everything else is fresh.