[authentication] clarify JWT availability in Local Server mode

Author: capcom6

docs/faq/local-server.md

@@ -32,4 +32,8 @@ Attempting to connect to the device's API directly can give you an immediate sen
 
 ## 🔑 How do I change my password in Local mode? :material-key:
 
-For Local mode, password management is handled through the [Server Configuration](../getting-started/local-server.md#server-configuration) section.
+For Local mode, password management is handled through the [Server Configuration](../getting-started/local-server.md#server-configuration) section.
+
+## 🔐 What authentication methods are supported in Local Server mode?
+
+Local Server mode **only supports Basic Authentication**. JWT authentication is not available in this mode. For JWT authentication, please use Public Cloud Server or Private Server modes.

docs/getting-started/local-server.md

@@ -13,6 +13,9 @@ This mode is ideal for sending messages from a local network, enabling direct co
 3. Tap the status button (labeled `Offline`) at the bottom of the screen to start the server; it will switch to `Online` when running.
 4. The `Local Server` section will display your device's local and public IP addresses, as well as the credentials for basic authentication.
 
+    !!! warning "Authentication Method"
+        Local Server mode **only supports Basic Authentication**. JWT authentication is not available in this mode.
+
     !!! note "Public IP Accessibility"
         The displayed public IP address is only accessible from the internet if your device has a public IP assigned by your ISP and your firewall/router allows connections to the specified port (with port forwarding configured). Many ISPs use Carrier-Grade NAT (CG‑NAT), which prevents direct internet access to devices behind shared addresses. See also: [FAQ — Local Server](../faq/local-server.md).