feat(ai): disable request storage via store:false parameter

Add store:false to AI API requests to prevent OpenAI, Perplexity, and
other providers from storing conversation data or using it for training.

Both the OpenAI Responses API and Perplexity API support the store
parameter to control whether requests are persisted. Setting it to false
ensures conversations remain private and are not retained by the provider.

Privacy:
- Requests are not stored by AI providers
- Conversations are not used for model training
- Aligns with CProof's privacy-first design

src/ai/ai_client.c

@@ -546,8 +546,9 @@ static gchar*
 _build_json_payload(AISession* session, const gchar* prompt)
 {
 
-    /* OpenAI-compatible format with messages array:
-     * {"model": "...", "messages": [...], "stream": false} */
+    /* OpenAI-compatible Responses API format:
+     * {"model": "...", "input": [...], "stream": false, "store": false}
+     * store:false prevents providers from storing/using requests for training */
     GString* messages_json = g_string_new("");
     GList* curr = session->history;
 
@@ -574,7 +575,7 @@ _build_json_payload(AISession* session, const gchar* prompt)
 
     auto_gchar gchar* escaped_model = ai_json_escape(session->model);
     gchar* json_payload = g_strdup_printf(
-        "{\"model\":\"%s\",\"input\":[%s],\"stream\":false}",
+        "{\"model\":\"%s\",\"input\":[%s],\"stream\":false,\"store\":false}",
         escaped_model, messages_json->str);
 
     g_string_free(messages_json, TRUE);