Health: count only flows the engine acts on, format durations with their unit

The "running" tile counted paused and invalid flows as running, so it read
"5/5" beside "1 flow(s) cannot run". Its note is now additive rather than a
precedence chain, so a quarantine no longer hides the invalid count.

Adds dur() beside si(): a ms reading picks its own unit, so a slow run reads
"1.24 s" instead of "1.2k ms".

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01HTsT1isxUjw5gtkJk8WhuA

backend/app/api/routes/observability.py

@@ -157,8 +157,18 @@ async def read_summary(
         problems=problems,
         flows={
             "total": len(names),
+            # What the engine will actually act on. Enabled is not enough:
+            # validation stops a flow as surely as quarantine does, and a
+            # paused one is holding its messages rather than running them.
             "running": len(
-                [n for n in names if controller.is_enabled(n) and n not in quarantined]
+                [
+                    n
+                    for n in names
+                    if controller.is_enabled(n)
+                    and n not in quarantined
+                    and n not in paused
+                    and n not in invalid
+                ]
             ),
             "paused": len(paused),
             "quarantined": len(quarantined),

backend/tests/api/routes/test_observability.py

@@ -91,6 +91,10 @@ def test_a_flow_that_cannot_run_makes_the_summary_degraded(
 
     controller = client.app.state.flow_controller
     before = controller.issues
+    before_flows = controller.store.list_flows
+    # The looping flow has to be one the store lists, otherwise "running"
+    # counts nothing either way and the assertion below proves nothing.
+    controller.store.list_flows = lambda: ["looping"]
     controller.issues = [
         ValidationIssue(
             code="cycle",
@@ -110,9 +114,11 @@ def test_a_flow_that_cannot_run_makes_the_summary_degraded(
         body = client.get(f"{PREFIX}/summary", headers=superuser_token_headers).json()
     finally:
         controller.issues = before
+        controller.store.list_flows = before_flows
 
     assert body["status"] == "degraded"
     assert body["flows"]["invalid"] == 1
+    assert body["flows"]["running"] == 0
     assert any("looping" in problem for problem in body["problems"])
     assert not any("broken" in problem for problem in body["problems"])
     assert not any("hooky" in problem for problem in body["problems"])