feat: complete calendar integration with UI improvements and code cleanup

Calendar Integration Tasks:
- Update upcoming meetings window from 30 to 120 minutes
- Include currently happening events in upcoming meetings API
- Create shared time utility functions (formatDateTime, formatCountdown, formatStartedAgo)
- Improve ongoing meetings UI logic with proper time detection
- Fix backend code organization and remove excessive documentation

UI/UX Improvements:
- Restructure room page layout using MinimalHeader pattern
- Remove borders from header and footer elements
- Change button text from "Leave Meeting" to "Leave Room"
- Remove "Back to Reflector" footer for cleaner design
- Extract WaitPageClient component for better separation

Backend Changes:
- calendar_events.py: Fix import organization and extend timing window
- rooms.py: Update API default from 30 to 120 minutes
- Enhanced test coverage for ongoing meeting scenarios

Frontend Changes:
- MinimalHeader: Add onLeave prop for custom navigation
- MeetingSelection: Complete layout restructure with shared utilities
- timeUtils: New shared utility file for consistent time formatting

🤖 Generated with [Claude Code](https://claude.ai/code)

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

www/app/lib/timeUtils.ts

@@ -0,0 +1,41 @@
+export const formatDateTime = (date: string | Date): string => {
+  const d = new Date(date);
+  return d.toLocaleString("en-US", {
+    month: "short",
+    day: "numeric",
+    hour: "2-digit",
+    minute: "2-digit",
+  });
+};
+
+export const formatCountdown = (startTime: string | Date): string => {
+  const now = new Date();
+  const start = new Date(startTime);
+  const diff = start.getTime() - now.getTime();
+
+  if (diff <= 0) return "Starting now";
+
+  const minutes = Math.floor(diff / 60000);
+  const hours = Math.floor(minutes / 60);
+  const days = Math.floor(hours / 24);
+
+  if (days > 0) return `Starts in ${days}d ${hours % 24}h ${minutes % 60}m`;
+  if (hours > 0) return `Starts in ${hours}h ${minutes % 60}m`;
+  return `Starts in ${minutes} minutes`;
+};
+
+export const formatStartedAgo = (startTime: string | Date): string => {
+  const now = new Date();
+  const start = new Date(startTime);
+  const diff = now.getTime() - start.getTime();
+
+  if (diff <= 0) return "Starting now";
+
+  const minutes = Math.floor(diff / 60000);
+  const hours = Math.floor(minutes / 60);
+  const days = Math.floor(hours / 24);
+
+  if (days > 0) return `Started ${days}d ${hours % 24}h ${minutes % 60}m ago`;
+  if (hours > 0) return `Started ${hours}h ${minutes % 60}m ago`;
+  return `Started ${minutes} minutes ago`;
+};