Add email notifications for reschedule flow

[teetangh]

Summary

The reschedule feature is functionally complete but lacks email notifications to keep both parties informed.

Current State

• ✅ Reschedule UI works (granular options: individual/multiple/entire sessions)
• ✅ Reschedule API works (marks slots as tentative, sets status to PENDING)
• ✅ Consultant can see reschedule requests in Requests tab
• ❌ No email notification when consultee requests reschedule
• ❌ No email notification when consultant approves new slots

Expected Behavior

When Consultee Initiates Reschedule

• Email to consultant: "[Consultee Name] has requested to reschedule their consultation on [date]. Please review and allocate new time slots."
• Include link to Requests tab

When Consultant Approves New Slots

• Email to consultee: "Your reschedule request has been approved. Your new consultation is scheduled for [date/time]."
• Include calendar invite or booking details

Files to Reference

• Reschedule API: /app/api/appointments/[appointmentId]/reschedule/route.ts
• Slot Allocation: /utils/slotAllocation/SlotAllocationService.ts
• Email templates: /lib/emails/

Acceptance Criteria

• Consultant receives email when consultee initiates reschedule
• Consultee receives email when consultant approves new slots
• Emails include relevant booking details (dates, times, consultant name)
• Emails include actionable links (Requests tab, booking confirmation)

[teetangh]

Already implemented — reschedule API calls notifyAppointmentRescheduled() for both parties (fire-and-forget).

[teetangh]

Reopened — notifyAppointmentRescheduled() exists but the issue may be about specific missing scenarios (staff-initiated, partial reschedule, etc.).

[teetangh]

Triage 2026-08-01 (from #1072 §6.4) — subset of #448, and partly shipped

Two things have changed since this was filed.

First, part of it exists. Verified against dev at 839d359c: an APPOINTMENT_RESCHEDULED Novu workflow is registered at lib/novu/workflows.ts:15, so the reschedule path is no longer entirely silent. The reschedule surfaces themselves were also substantially rebuilt in PR #1064 (dedicated pages, withdrawal, non-half-writing auto-confirm).

Second, #448 covers everything this issue asks for and more — the same two missing notifications, plus the audit trail, the staff and admin blind spots, and the UX gaps, all scoped against the current routes rather than the 2026-01 ones.

Recommended action: fold this into #448 and close it there via a Closes #337 on whichever PR does that work. Keeping both open splits the reschedule-notification work across two issues that will drift apart.

[teetangh]

Closing as a duplicate of #448.

The APPOINTMENT_RESCHEDULED Novu workflow this issue asks for now exists (lib/novu/workflows.ts). #448 covers the same notification gaps and additionally covers the reschedule audit trail and the staff/admin blind spots, so it is a strict superset of this issue.

No work is lost by closing this — track it in #448.

Closed as part of the backlog reconciliation in #1072 §6.4.