feat: the System tab reads a stored sample instead of inspecting per load (4295)

Operator: "there is a repull every time this page loads is there a reason
this info isn't being tracked in the background and stored in some way?"

There was a reason and it had expired, and underneath it there was plain
waste.

The expired one: /api/system/workers was deliberately uncached because an
operator dragging the stepper must not be shown a pre-change value. That
stopped being true at 1353d34, when the UI began patching its row from the
write's reply instead of refetching.

The waste: size_worker_lanes already inspected the broker on a timer to
decide pool sizes — computing the pool, active, reserved and queue depth
the page shows, using them, and discarding them. The browser then asked
the broker for the same numbers four times a minute, per open tab.

So one inspect now feeds three things: the sizing decision, a stored
sample (worker_lane_sample, alembic 0107), and the celery roster. No
request path touches the broker at all — the roster refresh comes off
/api/system/health too, where it had been rate-limited to 20s and so made
worker liveness a function of whether anyone had a browser open.

Consequences, stated rather than hidden:

- The live figures are up to one sweep old. measured_at travels with each
  lane and the page says how old, because a stale number presented as
  current is how someone watches a queue "not move" that is moving.
- The sweep is the roster's only writer now, so its period and the
  staleness thresholds are in a relationship. 60s against a 90s stale
  threshold left one missed tick between normal and all-yellow — the
  shape of lesson #4355 — so the period is 30s, named once in
  worker_lanes, and system_health asserts its headroom at import with a
  test stating the same thing in prose.
- An idle lane therefore also gives a worker back twice as fast. That is
  the direction asked for: "idle instances quiet down when not running".

Also bounds the inspect in push_lane_cap, which was an await with no
deadline (rule 156) — harmless while it ran on a request, less so now
that it runs in a background task where a hang would be silent.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LVjrnpQjRgHdvq95rASoiR

frontend/test/systemParts.spec.js

@@ -1,6 +1,6 @@
 import { describe, expect, it } from 'vitest'
 
-import { laneAdvice, mergeParts, queueKey } from '../src/utils/systemParts.js'
+import { laneAdvice, measuredAt, mergeParts, queueKey } from '../src/utils/systemParts.js'
 
 // The System tab's one table (operator 2026-09-23: "combine the two sections
 // into a single table"). What is pinned here is the JOIN, because its failure
@@ -190,3 +190,37 @@ describe('laneAdvice', () => {
     expect(laneAdvice(undefined)).toBeNull()
   })
 })
+
+
+// When the worker numbers were read. They stopped being fetched per page load
+// on 2026-09-23 — a sweep measures them on a timer and stores them — so the
+// age belongs on screen. Operator: *"is there a reason this info isn't being
+// tracked in the background and stored in some way?"*
+
+describe('measuredAt', () => {
+  it('reports the newest reading across the lanes', () => {
+    expect(measuredAt([
+      { measured_at: '2026-09-23T20:00:00Z' },
+      { measured_at: '2026-09-23T20:00:30Z' },
+      { measured_at: '2026-09-23T19:59:30Z' },
+    ])).toBe('2026-09-23T20:00:30Z')
+  })
+
+  it('ignores a lane the sweep has never written', () => {
+    // A lane added by a newer build, or a first boot mid-sweep. It must not
+    // drag the reported age back to null while other lanes have real ones.
+    expect(measuredAt([
+      { measured_at: null },
+      { measured_at: '2026-09-23T20:00:00Z' },
+    ])).toBe('2026-09-23T20:00:00Z')
+  })
+
+  it('says null when nothing has been measured, rather than guessing now', () => {
+    // The first period of a fresh install. "Not measured yet" and "measured
+    // just now" are opposite claims, and defaulting to the clock would make
+    // the page assert the wrong one at exactly the moment it knows least.
+    expect(measuredAt([{ measured_at: null }])).toBeNull()
+    expect(measuredAt([])).toBeNull()
+    expect(measuredAt(undefined)).toBeNull()
+  })
+})