feat: Show plan diffs when plan is updated during planning mode

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

When iterating on a plan in planning mode, there is no way to see what changed between iterations. After providing feedback and asking Claude to revise the plan, the entire updated plan is rendered — but the user has no visibility into the specific additions, removals, or modifications made.

This forces users to re-read the entire plan to identify what was actually changed, which becomes increasingly painful as plans grow in size and go through multiple revision cycles.

Proposed Solution

Show a diff view of plan changes when the plan is updated during planning mode, similar to how file edits display diffs during normal operation.

Possible approaches (non-exhaustive):

1. Inline diff on update — When the plan is revised, show a diff (added/removed/modified sections) instead of or alongside the full plan.
2. /plan-diff command — A command to view the diff between the current and previous version of the plan on demand.
3. Collapsible diff — Show the diff by default with the option to expand the full plan, or vice versa.

Use Case

• User enters planning mode and Claude generates a multi-phase plan
• User provides feedback: "move step 3 before step 2 and add error handling to phase 2"
• Claude updates the plan — user currently sees the full plan again and must manually find the changes
• With this feature: user sees a clear diff highlighting the reordering and the added error handling section

Related Issues

• #30438 — Broader plan mode rework proposal. This issue is a focused, independently shippable subset of that vision.
• #35796 — /plan preview command fails after update notification (related UX gap).
• #20899 — Plan file edits cluttering responses (closed, related UX concern).