feat: update authentication documentation and API access method to use await authManager.getApi()

Author: hotlong

content/docs/guides/authentication.mdx

@@ -46,7 +46,7 @@ The plugin uses a **direct forwarding** architecture where all authentication re
 - Full compatibility with all Better-Auth features
 - Minimal custom code to maintain
 - Easy updates when Better-Auth releases new features
-- Type-safe API access via `authManager.api`
+- Type-safe API access via `await authManager.getApi()`
 
 ---
 

packages/plugins/plugin-auth/ARCHITECTURE.md

@@ -105,7 +105,7 @@ rawApp.all('/api/v1/auth/*', async (c) => {
 **Solutions:**
 - Use Hono middleware for request interception if needed
 - Use better-auth plugins for custom behavior
-- Access `authManager.api` for programmatic operations
+- Access `await authManager.getApi()` for programmatic operations
 
 ## Results
 

packages/plugins/plugin-auth/README.md

@@ -181,7 +181,7 @@ This architecture provides:
 - ✅ **Full compatibility** - All better-auth features work automatically
 - ✅ **Easy updates** - Better-auth updates don't require code changes
 - ✅ **Type safety** - Full TypeScript support from better-auth
-- ✅ **Programmatic API** - Access auth methods via `authManager.api`
+- ✅ **Programmatic API** - Access auth methods via `await authManager.getApi()`
 
 #### ObjectQL Database Architecture