feat: approval decisions, tenant scoping, error paths with tests

- POST /api/approvals/{id}/decision (approve starts continuation flow
  with task facts; reject closes; 404/409/422 guards)
- Tenant scoping: list filters + cross-tenant reads 404
- Error mapping covered: LFX down 503, LFX drift 502, corrupt flow 422
- 34 tests green

backend/app/flows/api.py

@@ -34,6 +34,8 @@ from .lfx_client import (
 from .schemas import (
     ApprovalCreate,
     ApprovalRead,
+    DecisionRead,
+    DecisionRequest,
     FlowDefinitionCreate,
     FlowDefinitionRead,
     FlowImportRead,
@@ -290,9 +292,13 @@ async def _run_stream(session: Session, lfx: LfxClient, version, data: RunReques
 
 
 @flows_router.get("/{flow_id}/runs", response_model=list[RunRead])
-def list_runs(flow_id: UUID, session: Session = Depends(get_db)):
+def list_runs(
+    flow_id: UUID,
+    tenant_id: str | None = Query(default=None),
+    session: Session = Depends(get_db),
+):
     try:
-        return [_read_run(r) for r in store.list_runs(session, flow_id)]
+        return [_read_run(r) for r in store.list_runs(session, flow_id, tenant_id)]
     except store.NotFoundError as exc:
         raise HTTPException(status_code=404, detail=str(exc)) from exc
 
@@ -350,11 +356,19 @@ async def import_flow(
 
 
 @flows_router.get("/runs/{run_id}", response_model=RunRead)
-def get_run(run_id: UUID, session: Session = Depends(get_db)):
+def get_run(
+    run_id: UUID,
+    tenant_id: str | None = Query(default=None),
+    session: Session = Depends(get_db),
+):
+    """Read a run. With tenant_id, cross-tenant reads 404 (v1 scoping)."""
     try:
-        return _read_run(store.get_run(session, run_id))
+        run = store.get_run(session, run_id)
     except store.NotFoundError as exc:
         raise HTTPException(status_code=404, detail=str(exc)) from exc
+    if tenant_id is not None and run.tenant_id != tenant_id:
+        raise HTTPException(status_code=404, detail=f"run {run_id} not found")
+    return _read_run(run)
 
 
 @approvals_router.post("", response_model=ApprovalRead, status_code=201)
@@ -376,3 +390,66 @@ def list_approvals(
     session: Session = Depends(get_db),
 ):
     return [_read_task(t) for t in store.list_approval_tasks(session, tenant_id)]
+
+
+@approvals_router.post("/{task_id}/decision", response_model=DecisionRead)
+async def decide_approval(
+    task_id: UUID,
+    data: DecisionRequest,
+    session: Session = Depends(get_db),
+    lfx: LfxClient = Depends(get_lfx),
+):
+    """Decide an open task. Approve starts the continuation flow (if any)."""
+    try:
+        task = store.get_task(session, task_id)
+    except store.NotFoundError as exc:
+        raise HTTPException(status_code=404, detail=str(exc)) from exc
+
+    # Resolve the continuation first: bad references fail before any state change.
+    continuation_version = None
+    if data.decision == "approve" and task.continuation_flow_id is not None:
+        try:
+            continuation_version = store.get_latest_deployed_version(
+                session, task.continuation_flow_id
+            )
+        except (store.NotFoundError, store.InvalidError) as exc:
+            raise HTTPException(status_code=422, detail=str(exc)) from exc
+    try:
+        task = store.decide_task(
+            session,
+            task,
+            decision="approved" if data.decision == "approve" else "rejected",
+            approver=data.approver,
+            note=data.note,
+        )
+    except store.ConflictError as exc:
+        raise HTTPException(status_code=409, detail=str(exc)) from exc
+
+    # Note: the decision is committed before the continuation runs. If LFX is
+    # down, the task stays decided and the continuation can be started
+    # manually from the preserved task payload.
+    continuation_run = None
+    if continuation_version is not None:
+        payload = task.payload
+        if isinstance(payload.get("facts"), dict):
+            payload = payload["facts"]
+        try:
+            continuation_run = await runner.execute_run(
+                session,
+                lfx,
+                continuation_version,
+                payload=payload,
+                tenant_id=task.tenant_id,
+                session_id=f"continuation-of-{task.run_id}",
+                callback_base_url=data.callback_base_url or settings.callback_base_url,
+            )
+        except LfxNotFound as exc:
+            raise HTTPException(status_code=502, detail=f"LFX drift: {exc}") from exc
+        except LfxUnavailable as exc:
+            raise HTTPException(status_code=503, detail=str(exc)) from exc
+        except LfxError as exc:
+            raise HTTPException(status_code=502, detail=str(exc)) from exc
+    return DecisionRead(
+        task=_read_task(task),
+        continuation_run=_read_run(continuation_run) if continuation_run else None,
+    )