Choose which rack nozzle each filament prints from on an H2C (#1784)

The Vortek rack holds six hotends, and a multi-colour plate is sliced to
use a different one per colour so it can skip the purge. Which of the six
each colour takes is not in the 3MF. The same plate, sliced and sent twice
from Bambu Studio with a different choice each time, produces two files
that differ only in rounding in the last digit of a few extrusion figures
-- the filament grouping, the toolchange stream, the 120 nozzle-change
markers and project_settings.config are all identical. The choice travels
only in the dispatched nozzle_mapping.

Bambuddy had no way to state it, so those plates went out with no nozzle
assignment at all and the printer chose for itself. That is what levelled
on one hotend and printed with another, millimetres above the plate.

Every rack-bound filament now carries a position picker beside its AMS
slot dropdown, listing all six with the nozzle each holds. An empty
position, or one holding the wrong diameter or flow type, is shown greyed
out with the reason rather than hidden, so someone looking for position 4
finds it. The choice is per filament *group* rather than per slot, because
a group is one hotend: two filaments the slicer grouped together share it
and cannot point at different positions.

Nothing has to be picked. Positions are assigned automatically, preferring
one already loaded with that colour, which on the plate this was built
against reproduces Bambu Studio's own pick exactly.

A nozzle currently picked up onto the carriage is offered too. The
firmware drops its rack position from the report entirely rather than
sending a placeholder (#943), and refusing it would rule out the position
most likely to be wanted -- the one the last print left mounted. Only
recoverable when exactly one position is missing; two gaps are genuinely
ambiguous and stay unavailable.

Positions are re-checked at dispatch, not just when queued, because the
rack can be re-loaded in between. The two failure modes differ on purpose:
an explicitly chosen position that no longer fits stops the print, names
what the position now holds, and deletes the uploaded file from the SD
card so it cannot be started by hand either -- an operator who named a
hotend must not silently get a different one. An automatic assignment that
cannot be made instead falls back to letting the firmware choose, which is
what happened before any of this existed.

The pick is stored as {group: position} rather than as the expanded
nozzle_mapping, though that is what goes on the wire. That column means
"Bambu Studio decided, forward verbatim", and only the group-and-position
form can be re-checked against what is actually mounted at dispatch.

The existing multi-rack refusal in extract_nozzle_mapping_from_3mf stays.
It still guards the #2800 fallback, which can only ever name one rack id.

Measured on the maintainer's H2C: rack position n is physical nozzle id
15 + n, confirmed by cross-referencing two captured dispatches against
Bambu Studio's own dialog. extruder_max_nozzle_count names which carriage
is the rack straight from the file, and is read rather than assumed -- a
fourth independent confirmation of the carriage indices fixed in 45dc139.

The print dialog is also wider, on every printer. Its filament rows carry
the most horizontal content in it and adding a picker truncated names to
"Bamb...". The column widths themselves only change on a rack machine.

Tests: 44 unit covering the plan, the resolver, the mounted-nozzle
recovery and every refusal; 9 dispatch integration asserting the two real
captures end to end; 7 API round-trip; 33 frontend. The API ones exist
because two integration bugs got through a green suite that tested the
pieces and not the seams -- the group data reached only one of the three
filament-requirements routes, and the field was declared on every schema
except the create one, where Pydantic dropped it in silence.

backend/app/schemas/print_queue.py

@@ -60,6 +60,10 @@ class QueueVariantCreate(BaseModel):
     plate_id: int | None = None
     ams_mapping: list[int] | None = None
     nozzle_mapping: list[int] | None = None
+    # Which rack position each filament group prints from (#1784), as
+    # {group_id: 1-based position}. The operator's pick, re-checked against the
+    # live rack at dispatch; null means "assign them for me".
+    nozzle_rack_choice: dict[int, int] | None = None
     filament_overrides: list[dict] | None = None
 
 
@@ -116,6 +120,10 @@ class PrintQueueItemCreate(BaseModel):
     project_id: int | None = None
     cost_center_id: int | None = None
     estimated_cost: float | None = None
+    # Which rack position each filament group prints from (#1784), as
+    # {group_id: 1-based position}. The operator's pick, re-checked against the
+    # live rack at dispatch; null means "assign them for me".
+    nozzle_rack_choice: dict[int, int] | None = None
     # Direct printer-card uploads are temporary library files. The scheduler
     # deletes them after creating the durable archive copy.
     cleanup_library_after_dispatch: bool = False
@@ -157,6 +165,10 @@ class PrintQueueItemUpdate(BaseModel):
     # physical nozzle position IDs from BambuStudio's project_file MQTT
     # body; sent back to the printer verbatim on dispatch.
     nozzle_mapping: list[int] | None = None
+    # Which rack position each filament group prints from (#1784), as
+    # {group_id: 1-based position}. The operator's pick, re-checked against the
+    # live rack at dispatch; null means "assign them for me".
+    nozzle_rack_choice: dict[int, int] | None = None
 
 
 class QueueVariantSummary(BaseModel):
@@ -267,6 +279,10 @@ class PrintQueueItemResponse(BaseModel):
     # "edit print → choose nozzle" UI; null on every model except O1C2
     # uploads from BambuStudio.
     nozzle_mapping: list[int] | None = None
+    # Which rack position each filament group prints from (#1784), as
+    # {group_id: 1-based position}. The operator's pick, re-checked against the
+    # live rack at dispatch; null means "assign them for me".
+    nozzle_rack_choice: dict[int, int] | None = None
 
     class Config:
         from_attributes = True