feat: integrate Better Auth and enhance authentication flow

- Added Better Auth integration to the web application, allowing for dual login support with both custom and Better Auth systems.
- Updated authentication client configuration to dynamically set the base URL based on the environment.
- Enhanced chat components to utilize user authentication status, improving user experience and security.
- Refactored various components to support Better Auth, including error handling and user identity management.
- Improved notification handling and user feedback mechanisms during authentication processes.

apps/web/package.json

@@ -27,6 +27,7 @@
     "vite": "^7.1.2"
   },
   "dependencies": {
+    "@convex-dev/better-auth": "^0.9.7",
     "@dicebear/collection": "^9.2.4",
     "@dicebear/core": "^9.2.4",
     "@fullcalendar/core": "^6.1.19",
@@ -35,13 +36,16 @@
     "@fullcalendar/list": "^6.1.19",
     "@fullcalendar/multimonth": "^6.1.19",
     "@internationalized/date": "^3.10.0",
+    "@mmailaender/convex-better-auth-svelte": "^0.2.0",
     "@sgse-app/backend": "*",
     "@tanstack/svelte-form": "^1.19.2",
     "@types/papaparse": "^5.3.14",
+    "better-auth": "^1.3.34",
     "convex": "catalog:",
     "convex-svelte": "^0.0.11",
     "date-fns": "^4.1.0",
     "emoji-picker-element": "^1.27.0",
+    "is-network-error": "^1.3.0",
     "jspdf": "^3.0.3",
     "jspdf-autotable": "^5.0.2",
     "lucide-svelte": "^0.552.0",