fix(agent): count triage usage in the root token budget

Problem: an explicitly bounded root omitted billed command classifications
and external-content screening, allowing extra normal tool rounds.

Root cause: the shared triage terminal emitted usage without charging the
existing context-bound root counter.

Fix: observe terminal usage through the accepted private root helper before
the optional display guard. Preserve verdicts, screening notices, event
conditions, missing usage, normal telemetry and cancellation authority.

Verification: all 239 root packages pass in disjoint commands; full Agent
race and real boot HTTP/SSE matrices pass. The compiled preceding owner
fails ten events while five controls pass. Static gates, four platform
cross-compiles and the literal 15-event Windows contract pass locally.

.github/workflows/ci.yml

@@ -421,6 +421,36 @@ jobs:
           retention-days: 7
 
 
+      - name: test (Windows root triage budget)
+        if: env.RUN_STEPS == 'true' && runner.os == 'Windows' && github.event_name == 'pull_request'
+        timeout-minutes: 5
+        shell: bash
+        run: |
+          set -o pipefail
+          go test -count=1 -timeout=3m -json -run '^Test(RootTriage|EffectRootTriage)' ./internal/runtime/agent ./internal/assembly/boot | tee "$RUNNER_TEMP/root-triage-budget.jsonl"
+          jq -se '
+            [.[] | select(.Test == null and .Action == "pass") | .Package] as $packages |
+            [.[] | select(.Test != null and .Action == "pass") | .Test] as $tests |
+            all(.[]; .Action != "skip" and .Action != "fail") and
+            (["reasonix/internal/runtime/agent", "reasonix/internal/assembly/boot"] - $packages | length) == 0 and
+            (["TestRootTriageTokenBudget", "TestRootTriageTokenBudget/classifier", "TestRootTriageTokenBudget/screen",
+              "TestRootTriageTokenBudget/billed_failure", "TestRootTriageTokenBudget/missing", "TestRootTriageTokenBudget/disabled",
+              "TestRootTriageTokenBudget/no_sink", "TestRootTriageTokenBudget/counts_without_total",
+              "TestRootTriageOutsideRunDoesNotCreateScope", "TestEffectRootTriageScreenBudget",
+              "TestEffectRootTriageScreenBudget/reported", "TestEffectRootTriageScreenBudget/flagged",
+              "TestEffectRootTriageScreenBudget/disabled", "TestEffectRootTriageScreenBudget/missing",
+              "TestEffectRootTriageScreenBudget/screen_disabled"] - $tests | length) == 0
+          ' "$RUNNER_TEMP/root-triage-budget.jsonl"
+
+      - name: upload Windows root triage budget inventory
+        if: always() && env.RUN_STEPS == 'true' && runner.os == 'Windows' && github.event_name == 'pull_request'
+        uses: actions/upload-artifact@cf430e030ddbb5b0abf93d22962f4752f3646cd9 # v7
+        with:
+          name: root-triage-budget-windows-${{ github.run_attempt }}
+          path: ${{ runner.temp }}/root-triage-budget.jsonl
+          if-no-files-found: ignore
+          retention-days: 7
+
       - name: test (Windows root auxiliary budget)
         if: env.RUN_STEPS == 'true' && runner.os == 'Windows' && github.event_name == 'pull_request'
         timeout-minutes: 5