feat: add Help page with search, streamline copilot, misc UI fixes

Adds searchable Help/User Guide page, trims copilot tool bloat,
adds OTHER department option, and various form/layout improvements.

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

backend/prisma/migrations/20260207150425_add_other_department/migration.sql

@@ -0,0 +1,2 @@
+-- AlterEnum
+ALTER TYPE "Department" ADD VALUE 'OTHER';