$ psql -c "SHOW server_version"
16.15 (Ubuntu 16.15-0ubuntu0.24.04.1)

$ psql -c "SET timezone='Asia/Calcutta'"
ERROR:  invalid value for parameter "TimeZone": "Asia/Calcutta"

$ psql -c "SET timezone='Asia/Kolkata'"
SET

$ ls /usr/share/zoneinfo/Asia | grep -E 'Calcutta|Kolkata'
Kolkata

$ dpkg -l tzdata | tail -1
tzdata 2026e-0ubuntu0.24.04.1