Allow starting a fresh plan file mid-session instead of merging new plans into the existing auto-named file

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

In a single session, plan mode pins to one auto-named plan file. If I plan task A, implement it, and then in the same session enter plan mode to plan task B, the new plan gets merged into the original file rather than written to a new one. This causes two problems:

1. The new plan inherits items from the previous plan that are already implemented, so plan B is inaccurate and cluttered with completed work.
2. The original plan is overwritten, so I lose it as a record of what was implemented. I like to keep those for reference.

There's currently no way to create a separate, dedicated plan file from inside plan mode — the tool won't let me break away from the single auto-named file, even when asked.

Steps to reproduce current behavior:

1. Enter plan mode and create a plan for task A (file is auto-named).
2. Exit plan mode and implement task A.
3. Re-enter plan mode in the same session and ask to plan task B.
4. Observe: plan B is merged into A's file; A's original plan is gone and B includes A's completed items.

Proposed Solution

• Each new planning cycle in a session can write to its own plan file, preserving prior plans as a record.
• A way to explicitly start a new plan (and optionally name the file) from within plan mode.
• A new plan does not carry over already-implemented items from an earlier plan unless I ask it to.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

1. I start a Claude Code session and enter plan mode to plan a feature (Task A). Claude writes the plan to an auto-named file.
2. I exit plan mode and we implement Task A together.
3. Later in the same session, I enter plan mode again to plan a new, unrelated feature (Task B).
4. Instead of creating a fresh plan file, Claude merges Task B into the existing Task A file. The auto-named file is the only target and I can't create a separate one from inside plan mode.
5. Result: my original Task A plan is gone (I lose it as a record of what was planned and built), and the new Task B plan is polluted with Task A items that are already implemented — so the plan is inaccurate and cluttered.
6. With this feature, I could start a clean, separately-named plan file for Task B mid-session, keeping the Task A plan intact as a record and keeping Task B scoped to only what's actually new.
7. This would save me time because I wouldn't have to manually strip out already-completed items from the merged plan, and I'd retain a clean history of each planning cycle for reference.

Additional Context

_No response_