ui: round 8 — fuzzy session search, stacked doors, All right, teach divider at the step seam

- SESSION SEARCH goes fuzzy on the SAME fuzzyScore the model pickers
  use (de0c286's util — one scoring across every search surface):
  ranked by score instead of raw substring; empty query keeps order.
- SIDEBAR: New Teaching / New Practice STACK (full-width rows); the
  kind filter reads Teaching · Practice · All — the real modes first,
  All as the escape hatch, mirroring the stack above. Home stays in the
  LH band (owner-confirmed).
- TEACH DIVIDER, the stacked-dividers bug: the plan presentation and
  the first tagged quiz call usually share ONE assistant message, so
  the message-level seam drew Planning+Teaching back-to-back. New pure
  teachStepIndex(parts) finds the STEP boundary governing the flip
  call; the divider renders there (replacing that boundary's plain
  hairline — a labeled rule supersedes it), prepending before the whole
  message only when the flip is in its first step. The fold (chip,
  sidebar state) is untouched.
- JOBS SUITE, flake round 3: the sweep scans the SHARED jobs dir, so
  parallel test FILES' running records respawn into this file's
  counters — the assertions go jurisdictional (own-job ids collected;
  foreign respawns are not this test's business). 1331/1331.

src/core/phases.ts

@@ -96,6 +96,45 @@ function advance(
 	return phase;
 }
 
+/**
+ * WHERE inside the flipping message teaching begins (owner round 8,
+ * 2026-10-05 — the stacked-dividers bug): plan→teach flips at the first
+ * tagged quiz/explain CALL, but the plan PRESENTATION often lives in the
+ * same assistant message — an earlier provider STEP than the quiz call.
+ * A message-level seam therefore drew the Teaching divider before the
+ * plan presentation too (Planning and Teaching stacked back-to-back).
+ * This returns the part index of the STEP BOUNDARY governing the flip
+ * call: -1 when the call sits in the message's FIRST step (the divider
+ * belongs before the whole message), else the index of the step-start
+ * part whose generation contains the call — the divider renders there,
+ * between the plan presentation and the teaching block.
+ */
+export function teachStepIndex(
+	parts: ReadonlyArray<{ type: string; state?: string; input?: unknown }>,
+): number {
+	let stepStarts = 0; // how many step-start parts seen so far
+	let latest = -1; // index of the latest step-start
+	for (let i = 0; i < parts.length; i++) {
+		const part = parts[i]!;
+		if (part.type === "step-start") {
+			stepStarts++;
+			latest = i;
+			continue;
+		}
+		if (
+			(part.type === "tool-quiz" || part.type === "tool-explain") &&
+			taggedNodeId(part.input)
+		) {
+			// The call's governing step: 0–1 step-starts seen = the message's
+			// FIRST step → -1 (the divider belongs before the whole message);
+			// a later step → that step-start's index (the divider renders at
+			// the boundary, replacing the plain hairline there).
+			return stepStarts <= 1 ? -1 : latest;
+		}
+	}
+	return -1;
+}
+
 /**
  * The phase at EVERY message index, in one forward fold — the transcript
  * dividers render one per boundary, so phaseAt3(m, i) per index would rescan