v1.13.6: compaction head-assembly audit + reasoning fix

Audit traced compaction's summary path post-v1.13.1-B read flip:
- Q1: reads from messages_with_parts (view) — clean
- Q2: parts shape correctly threaded through buildHeadPayload — clean
- Q3: reasoning omitted from summary input — FIX NEEDED

v1.13.1-C wired reasoning end-to-end into inference/payload.ts but
missed this read site. Summarizer model couldn't see the reasoning
trail for tool-bearing turns, quietly degrading summary quality for
reasoning-channel models (qwen3.6).

Fix:
- CompactionMessage extended with reasoning_parts field
- SELECT pulls reasoning_parts from messages_with_parts
- buildHeadPayload (now exported for tests) prefixes assistant content
  with <reasoning>...</reasoning>\n\n<content>... when reasoning is
  present; standalone <reasoning>...</reasoning> for tool-call-only
  turns; omits the tag when reasoning is null or empty

4 new render branch tests (190 total).

Smoke deferred: forcing real compaction requires either threshold
pollution or building up a >40k-token chat with reasoning_parts.
Render branches are unit-covered; integration would only re-prove
structural correctness.

apps/server/src/services/__tests__/compaction.test.ts

@@ -6,6 +6,7 @@ import {
   turns,
   select,
   buildPrompt,
+  buildHeadPayload,
   type CompactionMessage,
 } from '../compaction.js';
 import { SUMMARY_TEMPLATE } from '../compaction-prompt.js';
@@ -31,6 +32,7 @@ function mkMsg(
     status: 'complete',
     tool_calls: null,
     tool_results: null,
+    reasoning_parts: null,
     metadata: null,
     created_at: new Date(counter * 1000).toISOString(),
     ...overrides,
@@ -256,3 +258,56 @@ describe('buildPrompt', () => {
     expect(out.endsWith('extra-context-line')).toBe(true);
   });
 });
+
+// ---- buildHeadPayload (v1.13.6) -----------------------------------------------
+
+describe('buildHeadPayload reasoning render', () => {
+  it('emits reasoning as a <reasoning> tag prefixed onto the assistant content', () => {
+    const out = buildHeadPayload([
+      mkMsg('user', 'show me the file'),
+      mkMsg('assistant', 'reading it now', {
+        reasoning_parts: [{ text: 'user wants src/index.ts; I should view it' }],
+      }),
+    ]);
+    expect(out).toHaveLength(2);
+    expect(out[1]!.role).toBe('assistant');
+    expect(out[1]!.content).toBe(
+      '<reasoning>user wants src/index.ts; I should view it</reasoning>\n\nreading it now',
+    );
+  });
+
+  it('emits a standalone <reasoning> tag when reasoning is present but content is empty (tool-call-only turn)', () => {
+    const out = buildHeadPayload([
+      mkMsg('assistant', '', {
+        reasoning_parts: [{ text: 'jumping straight to grep' }],
+        tool_calls: [{ id: 'c1', name: 'grep', args: { pattern: 'foo' } }],
+      }),
+    ]);
+    expect(out).toHaveLength(1);
+    expect(out[0]!.content).toBe('<reasoning>jumping straight to grep</reasoning>');
+    expect(out[0]!.tool_calls).toHaveLength(1);
+    expect(out[0]!.tool_calls![0]!.function.name).toBe('grep');
+  });
+
+  it('joins multiple reasoning parts without separators (matches the streaming concat)', () => {
+    const out = buildHeadPayload([
+      mkMsg('assistant', 'final answer', {
+        reasoning_parts: [{ text: 'first thought ' }, { text: 'second thought' }],
+      }),
+    ]);
+    expect(out[0]!.content).toBe(
+      '<reasoning>first thought second thought</reasoning>\n\nfinal answer',
+    );
+  });
+
+  it('omits the reasoning tag entirely when reasoning_parts is null or empty', () => {
+    const out = buildHeadPayload([
+      mkMsg('assistant', 'plain answer', { reasoning_parts: null }),
+      mkMsg('assistant', 'other answer', { reasoning_parts: [] }),
+    ]);
+    expect(out[0]!.content).toBe('plain answer');
+    expect(out[1]!.content).toBe('other answer');
+    expect(out[0]!.content).not.toContain('<reasoning>');
+    expect(out[1]!.content).not.toContain('<reasoning>');
+  });
+});