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.
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.
I'll have to try projects I guess, but I just want to sometimes ask questions without it bringing up shit I asked about in the past which isn't relevant to what I'm asking this time.
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.