feat(ams-backup): add status badge + toggle, fix prefer-lowest (#1766)

Two tightly-coupled deliverables in one drop -- a new AMS Filament Backup
  status/control surface, and the #1766 fix that depends on it.

  Added -- AMS Filament Backup status + control
  - Parse bit 18 of top-level print.cfg into PrinterState.ams_filament_backup
    on every push_status. Verified against OrcaSlicer source
    (DeviceManager.cpp:4961) and a live H2D ON/OFF capture. Tri-state
    (None = A1 family / pre-cfg push) preserves today's behaviour.
  - Hold-timer guard (3 s) prevents stale frames from flickering the badge
    back to the printer's old cfg after a user-initiated toggle.
  - POST /printers/{id}/ams-backup toggle, set_ams_filament_backup() client
    method calling _set_print_option("auto_switch_filament", enabled).
  - GET /printers/{id}/inventory-remain endpoint exposes the same map the
    dispatcher uses (internal and Spoolman modes both work uniformly).
  - Small icon badge in the printer card's "Filaments" section header
    (placement reads as printer-wide because the cfg bit is printer-wide,
    not per-AMS). Click to toggle, success toast.
  - 5 i18n keys x 11 locales for the badge UI.

  Fixed -- #1766: prefer_lowest didn't pick lowest, ignored backup state
  - Backend gate in _compute_ams_mapping_for_printer: coerce prefer_lowest
    to False when status.ams_filament_backup is False; log the skip.
  - New effectivePreferLowest(setting, backup) helper applied at every
    frontend sort entry point: single-printer PrintModal, multi-printer
    hook per-printer, PrinterSelector InlineMappingEditor, FilamentMapping
    standalone editor (the last had NO preferLowest awareness at all
    before this change).
  - New preferLowestSortKey(f, inventoryByTrayId) mirrors backend's two-tier
    key exactly, including the banding tie-break (regular AMS < AMS-HT <
    external) so the client-side pre-compute matches the dispatch-time pick.
    An earlier draft used a flat `amsId * 4 + trayId` priority which gave
    external slots (ams_id = -1) a NEGATIVE priority -- caught in code
    review before commit.
  - Settings -> Filament -> "Prefer lowest remaining filament" gets an
    explanatory note about the printer-side AMS Backup dependency, with
    i18n key in all 11 locales.

frontend/src/components/PrintModal/FilamentMapping.tsx

@@ -4,7 +4,7 @@ import { useQuery, useQueryClient } from '@tanstack/react-query';
 import { Circle, Check, AlertTriangle, RefreshCw, ChevronDown, ChevronUp, Palette } from 'lucide-react';
 import { api } from '../../api/client';
 import { useFilamentMapping } from '../../hooks/useFilamentMapping';
-import { getGlobalTrayId } from '../../utils/amsHelpers';
+import { getGlobalTrayId, effectivePreferLowest } from '../../utils/amsHelpers';
 import { getColorName } from '../../utils/colors';
 import { useFilamentLabels } from './useFilamentLabels';
 import type { FilamentMappingProps } from './types';
@@ -42,8 +42,35 @@ export function FilamentMapping({
     enabled: !!printerId,
   });
 
+  // Settings + inventory map drive the same prefer-lowest + AMS-backup gate
+  // the dispatcher uses (#1766). Without this, the per-slot dropdown's
+  // auto-suggestion could disagree with what actually gets dispatched.
+  const { data: settings } = useQuery({
+    queryKey: ['settings'],
+    queryFn: api.getSettings,
+  });
+  const { data: inventoryRemain } = useQuery({
+    queryKey: ['printer-inventory-remain', printerId],
+    queryFn: () => api.getInventoryRemain(printerId),
+    enabled: !!printerId,
+    staleTime: 30 * 1000,
+  });
+  const inventoryByTrayId = useMemo(() => {
+    if (!inventoryRemain?.inventory_remain_g) return undefined;
+    const map = new Map<number, number>();
+    Object.entries(inventoryRemain.inventory_remain_g).forEach(([key, grams]) => {
+      const gtid = Number(key);
+      if (!Number.isNaN(gtid)) map.set(gtid, grams);
+    });
+    return map;
+  }, [inventoryRemain]);
+  const gatedPreferLowest = effectivePreferLowest(
+    settings?.prefer_lowest_filament,
+    printerStatus?.ams_filament_backup,
+  );
+
   const { loadedFilaments, filamentComparison, hasTypeMismatch, hasColorMismatch } =
-    useFilamentMapping(filamentReqs, printerStatus, manualMappings);
+    useFilamentMapping(filamentReqs, printerStatus, manualMappings, gatedPreferLowest, inventoryByTrayId);
 
   // Per-slot sub-brand + material-disambiguated colour labels (#1718). Same
   // shared hook the model-mode FilamentOverride uses so both panels render

frontend/src/components/PrintModal/PrinterSelector.tsx

@@ -18,6 +18,7 @@ import {
   colorsAreSimilar,
   autoMatchFilament,
   filterFilamentsByNozzle,
+  effectivePreferLowest,
 } from '../../utils/amsHelpers';
 import type { PrinterSelectorProps, AssignmentMode } from './types';
 import type { PrinterMappingResult, PerPrinterConfig } from '../../hooks/useMultiPrinterFilamentMapping';
@@ -108,7 +109,13 @@ function InlineMappingEditor({
     } else {
       const usedTrayIds = new Set<number>(Object.values(printerResult.config.manualMappings));
       const cachedSettings = queryClient.getQueryData<{ prefer_lowest_filament?: boolean }>(['settings']);
-      loaded = autoMatchFilament(req, printerResult.loadedFilaments, usedTrayIds, cachedSettings?.prefer_lowest_filament) as LoadedFilament | undefined;
+      loaded = autoMatchFilament(
+        req,
+        printerResult.loadedFilaments,
+        usedTrayIds,
+        effectivePreferLowest(cachedSettings?.prefer_lowest_filament, printerResult.status?.ams_filament_backup),
+        printerResult.inventoryByTrayId,
+      ) as LoadedFilament | undefined;
     }
 
     // Determine status

frontend/src/components/PrintModal/index.tsx

@@ -1,4 +1,4 @@
-import { useMutation, useQuery, useQueryClient } from '@tanstack/react-query';
+import { useMutation, useQueries, useQuery, useQueryClient } from '@tanstack/react-query';
 import { AlertCircle, AlertTriangle, Calendar, Code, Layers, Loader2, Pencil, Printer, X } from 'lucide-react';
 import { useEffect, useMemo, useRef, useState } from 'react';
 import { useTranslation } from 'react-i18next';
@@ -15,7 +15,7 @@ import { getColorName } from '../../utils/colors';
 import { getCurrencySymbol } from '../../utils/currency';
 import { getBedTypeInfo } from '../../utils/bedType';
 import { toDateTimeLocalValue, parseUTCDate } from '../../utils/date';
-import { getGlobalTrayId, isPlaceholderDate } from '../../utils/amsHelpers';
+import { getGlobalTrayId, isPlaceholderDate, effectivePreferLowest } from '../../utils/amsHelpers';
 import { FilamentMapping } from './FilamentMapping';
 import { FilamentOverride } from './FilamentOverride';
 import { PlateSelector } from './PlateSelector';
@@ -270,6 +270,34 @@ export function PrintModal({
     enabled: ((mode === 'reprint' || mode === 'add-to-queue') && assignmentMode === 'printer') || (isLibraryFile && mode === 'reprint'),
   });
 
+  // Fetch per-printer Map<globalTrayId, gramsRemaining> via the dedicated
+  // backend endpoint (#1766). Server-side mirrors `_build_inventory_remain_overrides`
+  // so internal and Spoolman modes both work uniformly, VT/external slots are
+  // excluded, and negative grams are clamped — single source of truth between
+  // the client-side preview and dispatch-time picks.
+  const inventoryRemainQueries = useQueries({
+    queries: selectedPrinters.map((printerId) => ({
+      queryKey: ['printer-inventory-remain', printerId],
+      queryFn: () => api.getInventoryRemain(printerId),
+      staleTime: 30 * 1000,
+      enabled: selectedPrinters.length > 0,
+    })),
+  });
+  const inventoryByTrayIdPerPrinter = useMemo(() => {
+    const result = new Map<number, Map<number, number>>();
+    selectedPrinters.forEach((printerId, idx) => {
+      const data = inventoryRemainQueries[idx]?.data?.inventory_remain_g;
+      if (!data) return;
+      const printerMap = new Map<number, number>();
+      Object.entries(data).forEach(([key, grams]) => {
+        const gtid = Number(key);
+        if (!Number.isNaN(gtid)) printerMap.set(gtid, grams);
+      });
+      result.set(printerId, printerMap);
+    });
+    return result;
+  }, [selectedPrinters, inventoryRemainQueries]);
+
   // Fetch archive details to get sliced_for_model
   const { data: archiveDetails } = useQuery({
     queryKey: ['archive', archiveId],
@@ -346,8 +374,22 @@ export function PrintModal({
     enabled: !!effectivePrinterId,
   });
 
+  // Single-printer flow: gate prefer_lowest on this printer's backup state.
+  // Multi-printer flow gates per-printer inside the hook (different printers
+  // may have different backup states), so we pass the raw setting down.
+  const singlePrinterPreferLowest = effectivePreferLowest(
+    settings?.prefer_lowest_filament,
+    printerStatus?.ams_filament_backup,
+  );
+
   // Get AMS mapping from hook (only when single printer selected)
-  const { amsMapping } = useFilamentMapping(effectiveFilamentReqs, printerStatus, manualMappings, settings?.prefer_lowest_filament);
+  const { amsMapping } = useFilamentMapping(
+    effectiveFilamentReqs,
+    printerStatus,
+    manualMappings,
+    singlePrinterPreferLowest,
+    effectivePrinterId ? inventoryByTrayIdPerPrinter.get(effectivePrinterId) : undefined,
+  );
 
   // Multi-printer filament mapping (for per-printer configuration)
   const multiPrinterMapping = useMultiPrinterFilamentMapping(
@@ -358,6 +400,7 @@ export function PrintModal({
     perPrinterConfigs,
     setPerPrinterConfigs,
     settings?.prefer_lowest_filament,
+    inventoryByTrayIdPerPrinter,
   );
 
   // Auto-select first plate when plates load (single or multi-plate)