Add timezone selector to Admin settings with full-stack support

- Add `timezone` column to User model (VARCHAR 64, default UTC) with
  idempotent startup migration
- Expose and persist timezone via PATCH /api/users/me
- Fix TimerEvent.occurred_at serialization to include UTC offset marker
  (+00:00) so JavaScript correctly parses timestamps as UTC
- Add frontend utility (src/utils/time.js) with timezone-aware
  formatTime, getHHMM, getDateInTZ, tzDateTimeToUTC helpers and a
  curated IANA timezone list
- Add Settings section to Admin page with timezone dropdown; saves to
  both the API and localStorage for the unauthenticated TV view
- Update Activity Log to display and edit times in the user's timezone
- Update TV dashboard clock to respect the saved timezone
- Update README: features, setup steps, usage table, WebSocket events

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/app/models/user.py

@@ -12,6 +12,7 @@ class User(TimestampMixin, Base):
     full_name: Mapped[str] = mapped_column(String(255), nullable=False)
     is_active: Mapped[bool] = mapped_column(Boolean, default=True)
     is_admin: Mapped[bool] = mapped_column(Boolean, default=False)
+    timezone: Mapped[str] = mapped_column(String(64), nullable=False, default="UTC")
 
     children: Mapped[list["Child"]] = relationship("Child", back_populates="user")  # noqa: F821
     subjects: Mapped[list["Subject"]] = relationship("Subject", back_populates="user")  # noqa: F821