Start Drying was publishing a valid MQTT command that the firmware
silently refused. The per-AMS dry_sf_reason array was parsed but never
consulted before publish, so users with the AMS 2 Pro external PSU
unplugged (code 8) saw nothing happen. The empty filament field in our
payload was also a refusal trigger on some firmwares.
The /drying/start route now inspects dry_sf_reason and returns a 409
with a specific message, and backfills filament from the first loaded
tray (default PLA) so the printer can't reject the command for a
missing field.