feat: skill fast-path hardening, lineage retune + colors, per-tab pop-out, reliable tab alerts

- SKILL.md: forbid the standalone preamble check and pre-spawn recon turns
  (measured: two wasted model turns cost ~12s of a 28s two-worker run; the
  hardened flow measured 20.2s cold / 12.8s warm end to end)
- Lineage lines: dip now hangs from the strip's bottom edge (cap 104 -> 64,
  no stacked row offsets), fixing the deep bow in wrapped strips and keeping
  row-1 arcs off row-2 tab labels; per-child color palette (skin blue first,
  then matrix green, pink, violet, red, turquoise, orange) via an inline
  --lineage-color custom property
- Session Options -> Session: per-TAB pop-out (open-in-window) button override
  on top of the general showTabDetachButton setting; per-device localStorage
  map rendered as the tab-show-detach class
- Tab alerts: seed the pending-hook state machine from GET /api/approvals
  regardless of the approvals-inbox setting (reloads used to lose the red tab
  entirely with the inbox off), clear unconditionally on approval_resolved,
  and repaint the alert as a steady red/yellow ring + glow + status dot on a
  ::before overlay so it stays visible on the selected (active) tab until the
  permission is actually resolved
- docs: worker warm-pool design sketch (verified numbers baked in)

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

test/session-lineage-lines.test.ts

@@ -24,6 +24,7 @@ function loadLineageHelper() {
         DIP_MIN_PX: number;
         DIP_MAX_PX: number;
         SIBLING_STEP_PX: number;
+        COLORS: string[];
       };
     }
   ).CodemanLineage;
@@ -61,8 +62,9 @@ describe('lineage line geometry', () => {
     const near = helper.computePath({ parent: tab(0), child: tab(140), strip: STRIP })!;
     const far = helper.computePath({ parent: tab(0), child: tab(1000), strip: STRIP })!;
 
-    const nearDip = controlYs(near.d)[0] - 34;
-    const farDip = controlYs(far.d)[0] - 34;
+    // The dip hangs from the STRIP's bottom edge (40), not the tab bottoms.
+    const nearDip = controlYs(near.d)[0] - 40;
+    const farDip = controlYs(far.d)[0] - 40;
     expect(farDip).toBeGreaterThan(nearDip);
     expect(nearDip).toBeGreaterThanOrEqual(helper.DIP_MIN_PX);
     expect(farDip).toBeLessThanOrEqual(helper.DIP_MAX_PX);
@@ -80,15 +82,48 @@ describe('lineage line geometry', () => {
   it('keeps bending at strip-wide spans instead of flattening into a straight line', () => {
     const helper = loadLineageHelper();
     // A worker the agent skill starts is appended to the END of the strip, so this
-    // is the span the feature is actually used at. The first shipped clamp (44px)
-    // turned it into a flat thread across the terminal.
+    // is the span the feature is actually used at. The corridor has failed in BOTH
+    // directions: the first 44px clamp read as a flat thread here (#285), and the
+    // 104px clamp that replaced it bowed deep into the terminal (2026-08-15), so this
+    // pins the cap exactly rather than just a floor.
     const wide = helper.computePath({ parent: tab(0), child: tab(1300), strip: { ...STRIP, width: 1500 } })!;
     const near = helper.computePath({ parent: tab(0), child: tab(140), strip: STRIP })!;
 
-    const wideDip = controlYs(wide.d)[0] - 34;
-    const nearDip = controlYs(near.d)[0] - 34;
+    const wideDip = controlYs(wide.d)[0] - 40; // from the strip's bottom edge
+    const nearDip = controlYs(near.d)[0] - 40;
     expect(wideDip).toBeGreaterThan(nearDip * 2);
-    expect(wideDip).toBeGreaterThanOrEqual(80);
+    expect(wideDip).toBe(helper.DIP_MAX_PX);
+    expect(helper.DIP_MAX_PX).toBe(64);
+  });
+
+  it('hangs the dip from the STRIP bottom, so no per-row offset ever stacks on it', () => {
+    const helper = loadLineageHelper();
+    const twoRowStrip = { left: 0, top: 0, width: 1200, height: 84 }; // rows at y 4-34 and 48-78
+    // A wrapped pair (row 1 → row 2) and a same-row pair on ROW 1 of the same strip.
+    const wrapped = helper.computePath({ parent: tab(0), child: tab(400, 48), strip: twoRowStrip })!;
+    const row1Pair = helper.computePath({ parent: tab(0), child: tab(400), strip: twoRowStrip })!;
+
+    // Both brackets clear the ENTIRE strip: the wrapped one does not add the row
+    // offset on top (the 2026-08-15 over-bow), and the row-1 pair does not draw
+    // through row 2's tab labels (the retune's own first-draft regression).
+    for (const geom of [wrapped, row1Pair]) {
+      for (const y of controlYs(geom.d)) {
+        expect(y).toBeGreaterThanOrEqual(84 + helper.DIP_MIN_PX);
+        expect(y).toBeLessThanOrEqual(84 + helper.DIP_MAX_PX + helper.SIBLING_STEP_PX);
+      }
+    }
+  });
+
+  it('exposes a colour palette whose first entry defers to the skin blue', () => {
+    const helper = loadLineageHelper();
+    const colors = helper.COLORS;
+    expect(Array.isArray(colors)).toBe(true);
+    // '' = no override: session-lineage.js sets no inline --lineage-color and the
+    // CSS falls back to the skin-tuned --session-blue, so a lone arc stays blue.
+    expect(colors[0]).toBe('');
+    expect(colors.length).toBeGreaterThanOrEqual(6);
+    expect(new Set(colors).size).toBe(colors.length);
+    for (const c of colors.slice(1)) expect(c).toMatch(/^#[0-9a-f]{6}$/i);
   });
 
   it('brackets a wrapped pair BELOW the lower row rather than inside the row gap', () => {