Harden server security, rework landing page and refresh branding

Security:
- rooms: rate-limit /invite-email (SMTP spam relay), validate share
  target user exists, guard timingSafeEqual against length mismatch
  in the presentation route (500 -> 403)
- analytics: verify callback token before parsing the 5mb body so
  unauthenticated callers cannot buffer large payloads
- caldav: rate-limit failed Basic-Auth attempts (token brute force),
  lowercase email lookup, case-insensitive principal check
- auth: fall back to the in-memory rate-limit store when Redis is
  unavailable; previously every rate-limited endpoint (incl. login)
  returned 500 when the Redis connection was down

UI/copy:
- Home: factual hero copy and feature cards (6 instead of 9), fix
  double-rendered feature icon, remove fake stats row and pill badge;
  keep the background gradient and card layout
- i18n: consistent informal tone, drop trailing exclamation marks
  from status toasts, remove emoji from transactional emails
- new favicon (logo.svg), restore theme-based default brand logo

Chore:
- gitignore SQLite WAL/SHM files

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

public/logo.svg

@@ -0,0 +1,14 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512">
+  <!-- Speech bubble tail -->
+  <path d="M 185 325 L 148 425 L 248 360 Z" fill="#2B3140" stroke="#2B3140" stroke-width="14" stroke-linejoin="round"/>
+  <!-- Speech bubble outline -->
+  <circle cx="256" cy="240" r="120" fill="none" stroke="#2B3140" stroke-width="34"/>
+  <!-- Red dot -->
+  <circle cx="262" cy="234" r="76" fill="#ED2224"/>
+  <!-- Sound waves right -->
+  <path d="M 423 100 A 218 218 0 0 1 423 380" fill="none" stroke="#ED2224" stroke-width="32" stroke-linecap="round"/>
+  <path d="M 413 160 A 176 176 0 0 1 413 320" fill="none" stroke="#ED2224" stroke-width="30" stroke-linecap="round"/>
+  <!-- Sound waves left -->
+  <path d="M 89 100 A 218 218 0 0 0 89 380" fill="none" stroke="#ED2224" stroke-width="32" stroke-linecap="round"/>
+  <path d="M 99 160 A 176 176 0 0 0 99 320" fill="none" stroke="#ED2224" stroke-width="30" stroke-linecap="round"/>
+</svg>

public/vite.svg

@@ -1,5 +0,0 @@
-<svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" viewBox="0 0 32 32" fill="none">
-  <rect width="32" height="32" rx="8" fill="#ef4444"/>
-  <circle cx="16" cy="16" r="8" fill="white" opacity="0.9"/>
-  <circle cx="16" cy="16" r="4" fill="#ef4444"/>
-</svg>