Update User Timezone

Set the account's timezone. Every account type, one column.

Two things were wrong here until 2026-09-05, and together they are why 85% of accounts have no timezone at all:

• the parameter was a bare timezone_str: str, which FastAPI reads as a QUERY parameter. Both callers (DashboardNew, BookingsPage) send a JSON body, so every request 422'd before reaching the handler.
• for a student it wrote nothing and answered "Stored locally in browser". users.timezone is what quiet hours, the Word-of-the-Day send hour and every per-recipient time format read, so a student's choice reached none of them.

Tutors keep their tutor_profiles.timezone in step, because the booking surfaces read that one.