[FEATURE] Preserve and reuse thinking trace when user interrupts mid-thinking

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 Claude Code is in an extended thinking phase and the user interrupts (via Escape or by sending a new message), the entire thinking trace is discarded. If the model has spent significant compute generating a rich reasoning trace — analysing the codebase, evaluating approaches, building up intermediate conclusions — that work is thrown away entirely. The next turn starts from scratch with no memory of that reasoning.

This is wasteful in two ways:

1. Compute cost: Extended thinking tokens are expensive. Discarding them means paying for the same reasoning again on the next turn.
2. Quality loss: The interrupted thinking trace may contain valuable intermediate conclusions (e.g. "file X is the root cause", "approach B is better than A because…") that would improve the model's response if carried forward.

Proposed Solution

When a turn is interrupted while in the thinking phase (before any tool calls or response text has been produced), Claude Code should:

1. Capture the partial thinking trace accumulated so far.
2. Prepend it to the next turn's context — either as a thinking block in the message history, or as a summarised assistant note — so the model can build on rather than restart its reasoning.
3. Optionally surface a brief indicator in the UI: _"Resuming with prior thinking context"_ so the user knows the trace was preserved.

This is distinct from #39476 (which is about streaming thinking visibility in real-time). This request is specifically about the recycling of already-generated thinking tokens when the user sends a follow-up or correction mid-think, so that compute is not wasted and reasoning continuity is maintained.

Example Scenario

1. User sends a complex debugging request.
2. Model spends 30s in extended thinking, reasoning through 5 files, narrowing down to a likely root cause.
3. User interrupts to add: _"Also check the config loader, it was recently changed."_
4. Current behaviour: All 30s of thinking is discarded. Model restarts from scratch.
5. Desired behaviour: The thinking trace is preserved. The new message is appended. The model continues from where it left off, incorporating the new context without re-deriving everything it already reasoned through.

Alternative Solutions

• Summarise rather than replay: If the raw thinking blocks can't be replayed verbatim (due to API constraints on thinking block ordering), a summarised version of key conclusions from the interrupted trace could be injected as a user-visible or system note.
• Opt-in only: Gate this behind a config flag (e.g. preserveInterruptedThinking: true) for users who want the behaviour.

Related Issues

• #39476 — thinking visibility and correction queuing (related but distinct)
• #3074 — preserve plan progress on escape (similar spirit for planning phase)