fix(GRO-545): use socialProviders config key for GitHub/Google in Better-Auth

PR #257 placed google() and github() from better-auth/social-providers into
the plugins[] array. Better Auth v1 does not recognize social providers via
plugins — it reads them from options.socialProviders. This caused Provider
not found (404) on every GitHub/Google sign-in attempt.

Fix: move Google and GitHub configuration from plugins[] to socialProviders{},
passing clientId/clientSecret/redirectURI directly as plain config objects.
Better Auth v1 calls the internal provider factory functions automatically.

Also remove the now-unused import of google and github from
better-auth/social-providers.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/api/src/lib/auth.ts

@@ -1,7 +1,6 @@
 import { betterAuth } from "better-auth";
 import { drizzleAdapter } from "better-auth/adapters/drizzle";
 import { genericOAuth } from "better-auth/plugins";
-import { google, github } from "better-auth/social-providers";
 import { getDb, authProviderConfig, eq } from "@groombook/db";
 import { decryptSecret } from "@groombook/db";
 
@@ -173,22 +172,6 @@ export async function initAuth(): Promise<void> {
 
     const callbackBase = `${BETTER_AUTH_URL}/api/auth/callback`;
 
-    const socialPlugins = [];
-    if (hasGoogle) {
-      socialPlugins.push(google({
-        clientId: process.env.GOOGLE_CLIENT_ID!,
-        clientSecret: process.env.GOOGLE_CLIENT_SECRET!,
-        redirectURI: `${callbackBase}/google`,
-      }));
-    }
-    if (hasGitHub) {
-      socialPlugins.push(github({
-        clientId: process.env.GITHUB_CLIENT_ID!,
-        clientSecret: process.env.GITHUB_CLIENT_SECRET!,
-        redirectURI: `${callbackBase}/github`,
-      }));
-    }
-
     // Build Better-Auth instance using resolved config
     authInstance = betterAuth({
       database: drizzleAdapter(db, {
@@ -196,6 +179,22 @@ export async function initAuth(): Promise<void> {
       }),
       secret: BETTER_AUTH_SECRET,
       baseURL: BETTER_AUTH_URL,
+      socialProviders: {
+        ...(hasGoogle ? {
+          google: {
+            clientId: process.env.GOOGLE_CLIENT_ID!,
+            clientSecret: process.env.GOOGLE_CLIENT_SECRET!,
+            redirectURI: `${callbackBase}/google`,
+          },
+        } : {}),
+        ...(hasGitHub ? {
+          github: {
+            clientId: process.env.GITHUB_CLIENT_ID!,
+            clientSecret: process.env.GITHUB_CLIENT_SECRET!,
+            redirectURI: `${callbackBase}/github`,
+          },
+        } : {}),
+      },
       plugins: [
         genericOAuth({
           config: [
@@ -216,7 +215,6 @@ export async function initAuth(): Promise<void> {
             },
           ],
         }),
-        ...socialPlugins,
       ],
       session: {
         expiresIn: 60 * 60 * 24 * 7, // 7 days