Timezone conversion uses IANA library; no manual offset arithmetic

Manual offset arithmetic like date.getTime() + 5 * 3600000 hard-codes a fixed UTC offset and silently breaks twice a year during DST transitions. CWE-682 (Incorrect Calculation) and ISO 25010 functional correctness both flag this: New York is UTC-5 in January and UTC-4 in July — a hard-coded -5 produces a one-hour appointment time error for every booking during EDT. IANA libraries carry the full historical and future timezone rule database; manual arithmetic carries none of it. A single DST-related booking error can generate dozens of no-shows before anyone notices the pattern.

Replace all manual offset arithmetic with calls to an IANA-aware library. Install date-fns-tz (or luxon) and use its conversion functions exclusively throughout src/lib/.

// Bad — breaks during DST
const local = new Date(utc.getTime() - 5 * 3_600_000) // hardcoded EST offset

// Good — IANA library handles DST automatically
import { toZonedTime, fromZonedTime } from 'date-fns-tz'

const tz = 'America/New_York'
const localTime  = toZonedTime(utcDate, tz)   // display: UTC → local
const utcTime    = fromZonedTime(localDate, tz) // store:   local → UTC

Search src/ for the pattern * 3600000 or * 3_600_000 near timezone variables and replace each instance. Confirm date-fns-tz or equivalent appears in package.json dependencies, not just devDependencies.