After reading back through this thread, my guess would be your vehicle and mine are on the same ship.
356 A 0033TRCC is the number on mine and it’s also listed with the port of entry as TC. I believe TC is Tacoma.
355 on yours and 356 on mine are apparently the dates they were built, December 21 & 22.
Don’t know what the A means, the 003 I believe is the date they were shipped, the next 3 means they are 2023 model year. I don’t know what the T means but RCC is a vessel type, I believe it’s Regular Car Carrier.
Next I found this website
Free AIS Ship Tracker - VesselFinder
If you type in RCC, it brings up a whole bunch of ships that are vehicle carrying ships. I checked several of them for destination and found the RCC Antwerp is at sea and headed for Tacoma.
I hope this helps you.