auth: extract reusable sendVerificationEmail utility, enable sendOnSignUp

- Create src/lib/server/email-verification.ts with exported utility function
- Use it in auth.ts sendVerificationEmail callback
- Enable sendOnSignUp so verification email is sent on registration

src/lib/auth.ts

@@ -4,6 +4,7 @@ import { prisma } from '$lib/db';
 import { sveltekitCookies } from 'better-auth/svelte-kit';
 import { getRequestEvent } from '$app/server';
 import { sendMail } from './server/resend';
+import { sendVerificationEmail } from './server/email-verification';
 
 export const auth = betterAuth({
 	baseURL: process.env.BETTER_AUTH_URL,
@@ -11,14 +12,11 @@ export const auth = betterAuth({
 		provider: 'postgresql'
 	}),
 	emailVerification: {
+		sendOnSignUp: true,
 		sendVerificationEmail: async ({ user, url }) => {
-			void sendMail({
-				to: user.email,
-				templateId: 'email-verification-email',
-				data: {
-					target_email_address: user.email,
-					verification_link: url
-				}
+			void sendVerificationEmail({
+				email: user.email,
+				verificationUrl: url
 			});
 		}
 	},