feat: add search APIs and telegram-like chats sidebar flow

- implement chat query filtering and message search endpoints

- add db indexes for search fields

- activate chats search input in web

- replace inline create panel with floating TG-style action menu

web/src/api/chats.ts

@@ -2,8 +2,10 @@ import { http } from "./http";
 import type { Chat, ChatType, Message, MessageType } from "../chat/types";
 import axios from "axios";
 
-export async function getChats(): Promise<Chat[]> {
-  const { data } = await http.get<Chat[]>("/chats");
+export async function getChats(query?: string): Promise<Chat[]> {
+  const { data } = await http.get<Chat[]>("/chats", {
+    params: query?.trim() ? { query: query.trim() } : undefined
+  });
   return data;
 }
 
@@ -30,6 +32,16 @@ export async function getMessages(chatId: number, beforeId?: number): Promise<Me
   return data;
 }
 
+export async function searchMessages(query: string, chatId?: number): Promise<Message[]> {
+  const { data } = await http.get<Message[]>("/messages/search", {
+    params: {
+      query,
+      chat_id: chatId
+    }
+  });
+  return data;
+}
+
 export async function sendMessage(chatId: number, text: string, type: MessageType = "text"): Promise<Message> {
   const { data } = await http.post<Message>("/messages", { chat_id: chatId, text, type });
   return data;