[jhodapp]

Description

First of five PRs for the new stepped "New session" dialog (schedule + reschedule). This one adds the pure scheduling logic and copy the dialog will use, and pulls out three helpers so the dialog reuses existing code. No UI changes; nothing renders the new modules yet.

Changes

• src/lib/scheduling.ts: busy sessions on a day, slot overlap (touching edges are free), next free start, free half-hour slots within working hours (default 9–17), a person's usual slot (series start, else a weekday+time seen at least twice), suggested start times (usual → coach's frequent starts → round hours, free only, max 5), and step order for schedule/move modes.
• src/lib/scheduling-copy.ts: dialog labels (Who sub-lines, busy/overlap lines, repeat and submit labels, meeting-link line). Toasts scheduledMessage / rescheduledMessage go in session-change-message.ts.
• src/lib/people.ts: peopleFor, activityByPerson, menuPerson, initialsOf move out of the Join session menu hook unchanged, so the dialog can share them.
• Shared helpers: sessionEndIn and toSessionDate in session-window.ts (replaces 2 inline copies); sessionWriteFailure in lib/api/coaching-session-errors.ts (the session form's error-to-toast chain, same messages); duration field rules (clampDuration, 15–180 in steps of 5, chips 30/45/50/60).

Testing Strategy

• 69 new unit tests written as the spec before the code; all 2557 tests pass, tsc and lint clean.
• Behavior preserved: existing form, reschedule-series and Join session tests pass unedited.

Concerns

• The working-hours default is a constant until a setting exists (none in the backend today).