docs: use vapi.send add-message instead of nonexistent vapi.addMessage

fern/tools/client-side-websdk.mdx

@@ -12,7 +12,7 @@ Use the Web SDK to handle tool-calls entirely on the client. This lets your assi
 **In this guide, you'll learn to:**
 - Define a client-side tool with the Web SDK
 - Receive and handle `tool-calls` events on the client
-- Inject extra context during a call with `addMessage`
+- Inject extra context during a call with an `add-message` message
 
 <Warning>
 Client-side tools cannot send a tool "result" back to the model. If the model must use the output of a tool to continue reasoning, implement a server-based tool instead. See: <a href="https://docs.vapi.ai/tools/custom-tools" target="_blank">Server-based Function tools</a>.
@@ -32,7 +32,7 @@ npm install @vapi-ai/web
 
 2. Start a call with your tool defined in the <code>model.tools</code> array and subscribe to <code>clientMessages: ['tool-calls']</code>.
 3. Listen for <code>message.type === 'tool-calls'</code> and perform the desired UI update. No response is sent back to the model.
-4. (Optional) Inject context mid-call using <code>vapi.addMessage(...)</code>.
+4. (Optional) Inject context mid-call using `vapi.send({ type: 'add-message', ... })`.
 
 ## Complete example (React + Web SDK)
 
@@ -264,19 +264,25 @@ export default App;
 
 ## Inject data during the call
 
-Use <code>addMessage</code> to provide extra context mid-call. This does not return results for a tool; it adds messages the model can see.
+Send an <code>add-message</code> message with <code>vapi.send</code> to provide extra context mid-call. This does not return results for a tool; it adds messages the model can see. By default <code>triggerResponseEnabled</code> is set to <code>true</code> and the assistant should respond to the new message right away.
 
 ```ts
 // Inject system-level context
-vapi.addMessage({
-  role: 'system',
-  content: 'Context: userId=123, plan=premium, theme=dark',
+vapi.send({
+  type: 'add-message',
+  message: {
+    role: 'system',
+    content: 'Context: userId=123, plan=premium, theme=dark',
+  },
 });
 
 // Inject a user message
-vapi.addMessage({
-  role: 'user',
-  content: 'FYI: I switched to the settings tab.',
+vapi.send({
+  type: 'add-message',
+  message: {
+    role: 'user',
+    content: 'FYI: I switched to the settings tab.',
+  },
 });
 ```
 
@@ -289,7 +295,7 @@ If you need the model to <b>consume tool outputs</b> (e.g., fetch data and conti
 - **Client-only execution**: Omit the server URL to run tools on the client.
 - **One-way side effects**: Client tools do not send results back to the model.
 - **Subscribe to events**: Use <code>clientMessages: ['tool-calls']</code> and handle <code>message.type === 'tool-calls'</code>.
-- **Add context**: Use <code>vapi.addMessage</code> to inject data mid-call.
+- **Add context**: Use <code>vapi.send</code> with an <code>add-message</code> message to inject data mid-call.
 
 ## Next steps