[Bug] Command history bleeding across simultaneous Claude Code sessions

**Bug Description**
I'm running two Claude Code session simultaneously and the arrow-up history is bleeding across those two sessions. If you compare this to how shells work, you only get the history of other sessions when you load up a new shell. It's quite confusion and if this was meant to be a feature, I would like a setting to turn it off. Thanks!

**Environment Info**
- Platform: darwin
- Terminal: ghostty
- Version: 2.1.272
- Feedback ID: 9ffbd320-9fa5-4ffe-aebe-bf2bd4fdeda1

This looks related to https://github.com/anthropics/claude-code/issues/23276, which was dropped due to inactivity. Please take another look, thank you.

**Errors**
```json
[]
```

No source file or test is named. Start by locating the command-history handling and reproduce the behavior with two simultaneous Claude Code sessions on macOS, using the reported arrow-up workflow. Done means one session no longer exposes the other session's history, or an explicit opt-out setting is provided.

Written by the indexing model from the issue text.