Add better-auth integration and update dependencies in package.json and bun.lock

apps/web/package.json

@@ -23,10 +23,12 @@
     "vite": "^7.1.2"
   },
   "dependencies": {
+    "@convex-dev/better-auth": "^0.9.6",
+    "@mmailaender/convex-better-auth-svelte": "^0.2.0",
+    "@sgse-app/backend": "workspace:*",
     "@tanstack/svelte-form": "^1.19.2",
-    "zod": "^4.0.17",
     "convex": "catalog:",
     "convex-svelte": "^0.0.11",
-    "@sgse-app/backend": "workspace:*"
+    "zod": "^4.0.17"
   }
 }

apps/web/src/lib/auth.ts

@@ -0,0 +1,6 @@
+import { createAuthClient } from "better-auth/svelte";
+import { convexClient } from "@convex-dev/better-auth/client/plugins";
+
+export const authClient = createAuthClient({
+  plugins: [convexClient()],
+});

apps/web/src/routes/api/auth/[...all]/+server.ts

@@ -0,0 +1,3 @@
+import { createSvelteKitHandler } from "@mmailaender/convex-better-auth-svelte/sveltekit";
+
+export const { GET, POST } = createSvelteKitHandler();