[FEATURE] Surface expandable extended-thinking blocks in Cowork (parity with chat)

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

The Claude chat interface renders Claude's extended-thinking as inline, collapsible blocks — the reasoning summary plus the step/tool labels above it — so a user can expand any step and read how Claude approached the task before it commits.

Cowork (macOS desktop app) does not surface this. It shows progress indicators and a high-level approach summary, but not the expandable thinking blocks. As a result a Cowork user cannot:

• vet a research result by reading the reasoning that produced it;
• catch a wrong assumption before it propagates into file edits or multi-step execution;
• understand why Claude chose a given path during an autonomous run.

For document-heavy, high-stakes work (legal drafting, compliance, financial analysis) the reasoning trace is the primary trust and error-catching channel, so its absence in Cowork is a meaningful regression relative to chat.

This is scoped specifically to the Cowork desktop GUI. It is parallel to but distinct from #36006 (Claude Code CLI thinking toggle / Ctrl+O verbose mode — terminal, not the Cowork GUI) and #37441 (web-app reasoning effort control — how hard Claude reasons, not whether the reasoning is displayed). Cowork already supports ultrathink for per-turn high effort, which makes the lack of any way to see that reasoning more acute.

Proposed Solution

A collapsible thinking surface in Cowork matching the chat interface:

• expandable per-step thinking blocks (summarized chain-of-thought is fine — parity with chat, not raw tokens);
• the step/tool summary labels that sit above each block;
• collapsed by default to preserve Cowork's clean task view, expandable on click;
• persisted in the task transcript so reasoning can be reviewed after the run completes, not only live.

Alternative Solutions

Running the prompt in chat mode (gives the blocks but loses Cowork's autonomous file/multi-step execution) or in Claude Code CLI with Ctrl+O (terminal surface, not the Cowork GUI). Neither delivers the reasoning trace within the Cowork workflow itself.

Priority

High - Significant impact on productivity

Feature Category

Other

Use Case Example

When Cowork applies a batch of edits across a long document, it reasons about how to interpret the source before rewriting. In chat I would see that interpretation in a thinking block before any edit lands, so a wrong assumption could be caught and corrected at the reasoning step. In Cowork I see only progress lines like "Editing section 3…", so the faulty assumption stays invisible until it has propagated through every dependent section — turning a one-line correction into a full review and re-run. Seeing that reasoning inside Cowork would let me catch the error before edits commit.

Additional Context

The area:cowork label and Cowork-specific feature-request intake path now exist (see #38605, which re-filed a previously-closed Desktop request, #20041, once that path was established). This request uses the same intake for a Cowork-scoped gap that is currently unrepresented.