At the moment, Phuket Immigration is serving number 15, the queue issued yesterday. Anyone coming today without a number has to come back Monday. They're not giving queue numbers anymore.
No embassy letter was asked.
TLDR : Answer Summary
Phuket Immigration is currently serving queue number 15 from the previous day, and anyone without a number today will need to return on Monday, as no new queue numbers are being issued. Additionally, there was no requirement for an embassy letter.