fix(queue): persist "Print Anyway" so scheduler stops re-flagging it

When the user clicked Print Anyway on a filament-deficit warning, the
  acknowledgement was one-shot. The route cleared manual_start and
  filament_short, then the next scheduler tick re-ran
  compute_deficit_for_queue_item against identical spool state, found
  the same deficit, and re-set both flags. The item bounced between
  "user said anyway" and "scheduler re-blocked" — every Play click
  returned 409, every confirm got rolled back on the next tick.

  Add a persistent acknowledgement flag on the queue item:

  - New column `skip_filament_check` on print_queue. SQLite + Postgres
    migration branched on is_sqlite() so Postgres doesn't reject
    DEFAULT 0 on BOOLEAN.

  - PrintQueueItemCreate + PrintQueueItemResponse schemas + the
    TypeScript types carry the field.

  - POST /print-queue/{id}/start with skip_filament_check=true now
    ALSO sets item.skip_filament_check = True (not just clearing
    manual_start / filament_short).

  - PrintScheduler._block_on_filament_deficit short-circuits to
    False — no compute, no flag-setting, no notification — when
    item.skip_filament_check is True. We trust the operator's
    decision and stop fighting them.

  - PrintModal at queue-creation time threads
    skip_filament_check=true into the create payload when the user
    clicks Print Anyway on the frontend deficit warning, so a print
    that was warned-then-acknowledged at add-to-queue time goes in
    pre-acknowledged — scheduler never blocks it on first tick.

  Flag is not auto-cleared on spool swap by design: if remaining is
  now sufficient, the check returns no deficit anyway, so the flag
  is moot. Auto-clearing would add lifecycle complexity without
  changing behaviour.

  AMS Backup awareness (the other half of the discussion) intentionally
  NOT included — verified the H2D's bit-26 of print.cfg toggles with
  the printer-side AMS Backup setting, but the X1C's cfg has a
  different shape entirely and verifying every model family isn't
  realistic. Silently under-warning would be worse than always
  per-slot. The check stays single-slot for now.

backend/tests/integration/test_print_queue_api.py

@@ -147,6 +147,40 @@ class TestPrintQueueAPI:
         assert result["status"] == "pending"
         assert result["manual_start"] is True
 
+    @pytest.mark.asyncio
+    @pytest.mark.integration
+    async def test_add_to_queue_with_skip_filament_check(
+        self, async_client: AsyncClient, printer_factory, archive_factory, db_session
+    ):
+        """PrintModal "Print Anyway" persists skip_filament_check on creation (#1698-followup)."""
+        printer = await printer_factory()
+        archive = await archive_factory()
+
+        data = {
+            "printer_id": printer.id,
+            "archive_id": archive.id,
+            "skip_filament_check": True,
+        }
+        response = await async_client.post("/api/v1/queue/", json=data)
+        assert response.status_code == 200
+        result = response.json()
+        assert result["skip_filament_check"] is True
+
+    @pytest.mark.asyncio
+    @pytest.mark.integration
+    async def test_add_to_queue_skip_filament_check_defaults_false(
+        self, async_client: AsyncClient, printer_factory, archive_factory, db_session
+    ):
+        """Default add-to-queue has skip_filament_check=False — no silent bypass."""
+        printer = await printer_factory()
+        archive = await archive_factory()
+
+        data = {"printer_id": printer.id, "archive_id": archive.id}
+        response = await async_client.post("/api/v1/queue/", json=data)
+        assert response.status_code == 200
+        result = response.json()
+        assert result["skip_filament_check"] is False
+
     @pytest.mark.asyncio
     @pytest.mark.integration
     async def test_add_to_queue_with_project_id(
@@ -583,6 +617,53 @@ class TestQueueStartEndpoint:
         # decision to print anyway.
         assert called_with == {}
 
+    @pytest.mark.asyncio
+    @pytest.mark.integration
+    async def test_start_with_skip_flag_persists_acknowledgement(
+        self,
+        async_client: AsyncClient,
+        queue_item_factory,
+        db_session,
+    ):
+        """skip_filament_check=true sets the persistent flag on the queue item
+        so the scheduler doesn't re-flag it on the next tick (#1698-followup).
+
+        Without persistence the route's flag-clearing only survives until the
+        next scheduler tick re-runs the deficit check on identical spool
+        state and re-promotes the item — the user has to click Play+Confirm
+        every single tick.
+        """
+        item = await queue_item_factory(manual_start=True, filament_short=True)
+        assert item.skip_filament_check is False
+
+        response = await async_client.post(f"/api/v1/queue/{item.id}/start?skip_filament_check=true")
+        assert response.status_code == 200
+        body = response.json()
+        assert body["skip_filament_check"] is True
+
+        await db_session.refresh(item)
+        assert item.skip_filament_check is True
+
+    @pytest.mark.asyncio
+    @pytest.mark.integration
+    async def test_start_without_skip_flag_does_not_set_acknowledgement(
+        self,
+        async_client: AsyncClient,
+        queue_item_factory,
+        db_session,
+    ):
+        """A successful Play click with no deficit must NOT silently set the
+        acknowledgement flag — only an explicit Print Anyway should.
+        """
+        item = await queue_item_factory(manual_start=False, filament_short=False)
+        assert item.skip_filament_check is False
+
+        response = await async_client.post(f"/api/v1/queue/{item.id}/start")
+        assert response.status_code == 200
+
+        await db_session.refresh(item)
+        assert item.skip_filament_check is False
+
 
 class TestQueueCancelEndpoint:
     """Tests for the /queue/{item_id}/cancel endpoint."""