chat機能に通知機能を持たせる２

chatコントローラー

class Public::ChatsController < ApplicationController
  before_action :authenticate_user!
  before_action :set_user_and_room, only: [:show]

  def show
    @chats = @room.chats
    @chat = Chat.new(room_id: @room.id)
  end

  def create
    @chat = current_user.chats.new(chat_params)
    @chat.save
  end

  private

  def set_user_and_room
    @user = User.find(params[:user_id])
    @room = find_or_create_room
  end

  def find_or_create_room
    rooms = current_user.user_rooms.pluck(:room_id)
    user_room = UserRoom.find_by(user_id: @user.id, room_id: rooms)
    return user_room.room if user_room
    create_new_room
  end

  def create_new_room
    room = Room.create
    UserRoom.create(user_id: @user.id, room_id: room.id)
    UserRoom.create(user_id: current_user.id, room_id: room.id)
    room
  end

  def chat_params
    params.require(:chat).permit(:message, :room_id)
  end
end

show.html.erb

<div class="container">
    <div class="row">
        <div class="col-xs-6">
            <h2>CHAT ROOM </h2>

            <table class="table">
              <thead>
                <tr>
                  <th style="text-align: left; font-size: 20px;"><%= current_user.username %></th>
                  <th style="text-align: right; font-size: 20px;"><%= @user.username %></th>
                </tr>
              </thead>
              <tbody id="messages">
                <% @chats.each do |chat| %>
                  <%= render 'message', chat: chat %>
                <% end %>
              </tbody>
            </table>
           <%= form_with model: @chat, url: public_user_chats_path, local: false do |f| %>
              <div class="arrow_box">
                <%= f.text_field :message %>
              </div>
              <%= f.hidden_field :room_id %>
              <button type="submit" class="btn btn-sm btn-success chat-btn">SEND</button>
            <% end %>
        </div>
    </div>
</div>

_message.html.erb

<tr>
    <% if chat.user == current_user %>
        <th>
          <p style="text-align: left;" class="m-0 arrow_box"><%= chat.message %></p>
        </th>
        <th></th>
    <% else %>
        <th></th>
        <th>
            <p style="text-align: right;" class="m-0 arrow_box2"><%= chat.message %></p>
        </th>
    <% end %>
</tr>

create.js

$('#messages').append('<%= j(render 'message', chat: @chat) %>')
$('#chat_message').val('')

route.rb

resources :notifications, only: [:update]

chatのルートは参照したものに載っているはずです。
これで通知機能としては動くはずです。