Show which Filament Track Switch inlet each AMS feeds

With a switch fitted, an AMS is not wired to a nozzle any more. It is
plumbed into one of the switch's two inlets and reaches both nozzles
through it, so every unit reports its extruder as "not fixed" (0xE) and
ams_extruder_map comes back empty on these machines.

The printer card had nothing to fall back on but the AMS unit number, so
AMS-A was badged R and AMS-B was badged L purely because their unit ids
are 0 and 1, a third unit got no badge at all, and every one of those
labels was wrong. The SpoolBuddy assign modal had the same fallback in a
worse form, mapping anything that was not extruder 1 to R.

The binding turned out to need no new telemetry. BambuStudio reads it out
of bits 24-27 of the same AMS info string we already parse for the AMS
type and the extruder id -- 0 is In-B, 1 is In-A -- and it is only
meaningful when a switch is installed, because without one 0xE really
does mean an uninitialised unit and those bits carry nothing. That gates
the read, which in turn forced the switch block to be parsed before the
AMS block: _handle_ams_data runs early in _process_message and
_update_state only much later, so the binding was lost on every frame
that carried both. _parse_fila_switch is split out and called first, and
left in _update_state as well so that stays a complete absorb step.

The badge keeps L and R rather than A and B, because the lettering is
familiar and matches the physical layout. It is a different colour from
the plain nozzle badge, and its tooltip names the inlet in full, since
the letter is the inlet's position and not a claim about which nozzle
that AMS feeds -- the switch can route either inlet to either outlet. An
AMS still reporting a real extruder id keeps its ordinary badge, which
BambuStudio also treats as authoritative over any switch binding, and a
switch that has been fitted but not yet set up on the printer shows
nothing rather than a guess.

The print dialog's slot dropdown gets the same label. It replaces a
left/right hint that never once rendered: ftsExtruderForSlot compared
snow-encoded in[] values against global tray ids and could not match.
Decoding it correctly would not have saved it -- the firmware reports
which slot sits in each inlet and which nozzle each outlet feeds, but
never which inlet is currently paired with which outlet, so no per-slot
nozzle can be derived. That function is gone rather than fixed.

The dialog also points out when every filament a print needs sits behind
one inlet. Bambu's own guidance is that this is legal but slow: a change
between two filaments on the same inlet retracts the outgoing spool all
the way back to its AMS before the next can be fed up the shared tube,
where a change across the two inlets only retracts as far as the switch.
All on one inlet means every change in the job takes the slow path, and
moving a single spool fixes it. So it advises, it does not block.

Both views update live. Two things were stopping that. fila_switch and
ams_switch_inlet were absent from printer_state_to_dict, and the frontend
shallow-merges each WebSocket push over its cached status, so a field the
push omits keeps whatever the last full fetch left behind. And the
broadcast dedup key had no term for either, so "Join IN-B" on the printer
screen moved nothing: the binding is not in the tray component of that
key, and it is not in the AMS change-hash either, which covers tray
fields only and must stay that way because it drives Spoolman sync.

Assigning an AMS to an inlet remains printer-side. BambuStudio can read
the binding and has no command to write it -- its switch class is parse
and getters only, and the recommended-arrangement popup draws and
publishes nothing -- so there is no wire format for us to copy.

Adding the two fields to PrinterState broke four test modules whose
SimpleNamespace stubs predate them. The stubs are fixed rather than the
production reads made defensive: the real dataclass always carries both,
and a getattr in the dedup key would silently stop tracking the field if
it were ever renamed.

frontend/src/api/client.ts

@@ -492,14 +492,21 @@ export interface PrintOptions {
 
 export interface FilaSwitchState {
   installed: boolean;
-  // in[track] = currently loaded slot for that track (-1 = empty)
+  // Raw wire arrays, ordered **In-B first, then In-A** (BambuStudio's SwitchPos
+  // enum). in[] values are snow-encoded (bits 8-15 = AMS id, bits 0-7 = slot,
+  // -1 = empty); out[] values are the extruder each *outlet* terminates at, or
+  // 0xE when unset. Neither array says which inlet is currently routed to which
+  // outlet — that pairing is not reported. For per-AMS side information use
+  // PrinterStatus.ams_switch_inlet instead.
   in_slots: number[];
-  // out[track] = extruder this track terminates at (0 = right, 1 = left)
   out_extruders: number[];
   stat: number;
   info: number;
 }
 
+// Which FTS inlet an AMS is plumbed into: 'A' | 'B'.
+export type FtsInlet = 'A' | 'B';
+
 export interface PrinterStatus {
   id: number;
   name: string;
@@ -565,6 +572,11 @@ export interface PrinterStatus {
   // AMS slots aren't tied to a specific extruder; the FTS routes any slot to
   // either extruder, so per-extruder slot filtering must be skipped.
   fila_switch: FilaSwitchState | null;
+  // Per-AMS FTS inlet binding, {ams_id: 'A' | 'B'}, as set on the printer's
+  // "Manual AMS Setup" screen. Empty unless a switch is installed. An AMS with
+  // an entry here reaches BOTH nozzles through the switch, which is why it has
+  // no ams_extruder_map entry and must not be badged left or right.
+  ams_switch_inlet: Record<string, FtsInlet>;
   // Currently loaded tray (global tray ID, 255 = no filament loaded, 254 = external spool)
   tray_now: number;
   // Runout / filament-replacement guidance (#2587). Populated only while PAUSED.