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/src/utils/systemParts.js

@@ -142,3 +142,25 @@ export function laneAdvice(lane) {
     + `Raise the cap to run more at once — this machine allows up to `
     + `${lane.ceiling}.`
 }
+
+
+// When the worker numbers in the table were actually read.
+//
+// They used to be fetched live on every page load — a celery broadcast per
+// request, on a page that polls every 15s. Operator, 2026-09-23: *"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?"* It is now: a sweep
+// measures on a timer and stores it, and the page reads the table.
+//
+// So the age has to be ON SCREEN. A number that is up to half a minute old,
+// presented as current, is how someone ends up watching a queue "not move"
+// that is in fact moving. The NEWEST across lanes, because they are written
+// by one sweep in one pass — a lane lagging the others means its row has
+// never been written, and that lane says so in its own detail line.
+export function measuredAt(lanes) {
+  const stamps = (lanes || [])
+    .map((l) => l.measured_at)
+    .filter(Boolean)
+    .sort()
+  return stamps.length ? stamps[stamps.length - 1] : null
+}