コメント件数をリロードせずに更新させたい

前提・実現したいこと

コメント件数がリロードしないと更新できない。
本の感想アプリを作っています。
その他、いいね機能押し外し、コメント機能の投稿、削除は全て動作している。

発生している問題・エラーメッセージ

コメント件数がリロードしないと更新できない。
ブラウザ等にエラー文がない状態です。
一応、コメントを投稿した際と削除した際のターミナル出力情報を下記に記載します。

該当のソースコード

ターミナル(create時)

Started POST "/books/2/book_comments" for 14.10.133.132 at 2021-07-29 10:11:01 +0000
Cannot render console from 14.10.133.132! Allowed networks: 127.0.0.1, ::1, 127.0.0.0/127.255.255.255
Processing by BookCommentsController#create as JS
  Parameters: {"utf8"=>"✓", "authenticity_token"=>"VyxutmVOteHR9UwmCyf2QrAecUbNsKskoE3jkGuP9Ld4bWALMHoBR8rNFSyd1iVnLykFJ4-KWkJitfaXctAsAA", "book_comment"=>{"comment"=>"いいいいい"}, "commit"=>"送信", "book_id"=>"2"}
  User Load (0.1ms)  SELECT  "users".* FROM "users" WHERE "users"."id" = ? ORDER BY "users"."id" ASC LIMIT ?  [["id", 5], ["LIMIT", 1]]
  ↳ /home/ec2-user/.rvm/gems/ruby-2.6.3/gems/activerecord-5.2.5/lib/active_record/log_subscriber.rb:98
  Book Load (0.1ms)  SELECT  "books".* FROM "books" WHERE "books"."id" = ? LIMIT ?  [["id", 2], ["LIMIT", 1]]
  ↳ app/controllers/book_comments_controller.rb:6
   (0.1ms)  begin transaction
  ↳ app/controllers/book_comments_controller.rb:10
  User Load (0.1ms)  SELECT  "users".* FROM "users" WHERE "users"."id" = ? LIMIT ?  [["id", 5], ["LIMIT", 1]]
  ↳ app/controllers/book_comments_controller.rb:10
  BookComment Create (1.3ms)  INSERT INTO "book_comments" ("comment", "user_id", "book_id", "created_at", "updated_at") VALUES (?, ?, ?, ?, ?)  [["comment", "いいいいい"], ["user_id", 5], ["book_id", 2], ["created_at", "2021-07-29 10:11:01.398246"], ["updated_at", "2021-07-29 10:11:01.398246"]]
  ↳ app/controllers/book_comments_controller.rb:10
   (4.5ms)  commit transaction
  ↳ app/controllers/book_comments_controller.rb:10
  Rendering book_comments/index.js.erb
  BookComment Load (0.2ms)  SELECT "book_comments".* FROM "book_comments" WHERE "book_comments"."book_id" = ?  [["book_id", 2]]
  ↳ app/views/book_comments/_index.html.erb:2
  User Load (0.1ms)  SELECT  "users".* FROM "users" WHERE "users"."id" = ? LIMIT ?  [["id", 3], ["LIMIT", 1]]
  ↳ app/views/book_comments/_index.html.erb:5
  Rendered book_comments/_index.html.erb (16.0ms)
  Rendered book_comments/index.js.erb (19.5ms)
Completed 200 OK in 49ms (Views: 25.4ms | ActiveRecord: 6.6ms)

ターミナル(destroy時)

Started DELETE "/books/2/book_comments/161" for 14.10.133.132 at 2021-07-29 10:11:39 +0000
Cannot render console from 14.10.133.132! Allowed networks: 127.0.0.1, ::1, 127.0.0.0/127.255.255.255
Processing by BookCommentsController#destroy as JS
  Parameters: {"book_id"=>"2", "id"=>"161"}
  User Load (0.1ms)  SELECT  "users".* FROM "users" WHERE "users"."id" = ? ORDER BY "users"."id" ASC LIMIT ?  [["id", 5], ["LIMIT", 1]]
  ↳ /home/ec2-user/.rvm/gems/ruby-2.6.3/gems/activerecord-5.2.5/lib/active_record/log_subscriber.rb:98
  BookComment Load (0.1ms)  SELECT  "book_comments".* FROM "book_comments" WHERE "book_comments"."id" = ? LIMIT ?  [["id", 161], ["LIMIT", 1]]
  ↳ app/controllers/book_comments_controller.rb:37
   (0.1ms)  begin transaction
  ↳ app/controllers/book_comments_controller.rb:38
  BookComment Destroy (0.2ms)  DELETE FROM "book_comments" WHERE "book_comments"."id" = ?  [["id", 161]]
  ↳ app/controllers/book_comments_controller.rb:38
   (6.2ms)  commit transaction
  ↳ app/controllers/book_comments_controller.rb:38
  Rendering book_comments/index.js.erb
  Book Load (0.1ms)  SELECT  "books".* FROM "books" WHERE "books"."id" = ? LIMIT ?  [["id", 2], ["LIMIT", 1]]
  ↳ app/views/book_comments/index.js.erb:2
  BookComment Load (0.1ms)  SELECT "book_comments".* FROM "book_comments" WHERE "book_comments"."book_id" = ?  [["book_id", 2]]
  ↳ app/views/book_comments/_index.html.erb:2
  User Load (0.1ms)  SELECT  "users".* FROM "users" WHERE "users"."id" = ? LIMIT ?  [["id", 3], ["LIMIT", 1]]
  ↳ app/views/book_comments/_index.html.erb:5
  Rendered book_comments/_index.html.erb (15.2ms)
  Rendered book_comments/index.js.erb (21.5ms)
Completed 200 OK in 45ms (Views: 28.1ms | ActiveRecord: 6.9ms)

bookの詳細を載せるページ/bookers2-debug/app/views/books/show.html.erb

<div class='container'>
  <div class='row'>
    <div class='col-md-3'>
      <h2>User info</h2>
      <%= render 'users/info',user: @user %>
      <h2 class="mt-3">New book</h2>
      <%= render 'form', book: @new_book,user: @user %>
    </div>
    <div class='col-md-8 offset-md-1'>
  		<h2>Book detail</h2>



  		<table class='table'>

  　　　　　　　　<tr>
 　　　　　　　　　　　　　　　　　　<td><%= link_to user_path(@book.user) do %>
            <%= attachment_image_tag(@book.user, :profile_image, :fill, 100, 100, fallback: "no-image-icon.jpg") %><br>
            <%= @book.user.name %>
            <% end %>
          </td>
          <td><%= link_to @book.title, book_path(@book) %></td>
          <td><%= @book.body %></td>


          <td >
            <div id="favorites_buttons_<%= @book.id %>" >
             <%= render 'favorites/favorite-btn', book: @book %>
            </div>
          </td>

      
          
          <td>
           <p>コメント数：<%= @book.book_comments.count %></p>(ここのコメント件数が変わって欲しい)
          </td>
          
          <% if @book.user==current_user %>
          <td><%= link_to 'Edit', edit_book_path(@book), class: "btn btn-sm btn-success edit_book_#{@book.id}" %></td>
          <td><%= link_to 'Destroy', book_path(@book), method: :delete, data: { confirm: '本当に消しますか？' }, class: "btn btn-sm btn-danger destroy_book_#{@book.id}"%></td>
          <% end %>
        </tr>
      </table>

      <div id="comment_create">

        <%= render partial: 'book_comments/index', locals: { book_comments: @book_comments } %>
      </div>

      <div id="comment_create">

        <%= render partial: 'book_comments/form', locals: { book_comment: @book_comment, book: @book } %>
      </div>





  </div>
</div>

/bookers2-debug/app/views/book_comments/index.js.erb

$("#comment_create").html("<%= j(render 'index', { book_comments: @book_comment.book.book_comments }) %>");
$("textarea").val('');

/bookers2-debug/app/views/book_comments/_index.html.erb

<table class='table'>
        <% book_comments.each do |book_comment| %>
        <tr>

          <td><%= link_to user_path(book_comment.user.id) do %>
            <%= attachment_image_tag(book_comment.user, :profile_image, :fill, 40, 40, fallback: "no-image-icon.jpg") %><br>
            <%= book_comment.user.name %>
            <% end %>
          </td>
          <td>
            <%= book_comment.comment %>
          </td>

          <% if book_comment.user == current_user %>
          <td>
            <%= link_to "Destroy", book_book_comment_path(book_comment.book_id, book_comment.id ), method: :delete,remote: true,class: "btn btn-sm btn-danger" %>
          
          </td>
          <% end %>

        </tr>
        <% end %>
  </table>

/bookers2-debug/app/views/book_comments/_form.html.erb

<%= form_with(model: [book, book_comment], url: book_book_comments_path(book) ) do |f| %>
    <%= f.text_area :comment, class: "input-mysize", size: "60x5" %>
    <div>
    <%= f.submit "送信", class: "btn btn-outline-dark comment-submit float-right" %>
    </div>
<% end %>

/bookers2-debug/app/controllers/book_comments_controller.rb

def create
    @book = Book.find(params[:book_id])
    @book_comment = @book.book_comments.build(book_comment_params)
    @book_comment.user_id = current_user.id
   
    @book_comment.save!
    render :index

end



  def destroy
   
    @book_comment = BookComment.find(params[:id])
    @book_comment.destroy
    render :index
  end

  private

  def book_comment_params
    params.require(:book_comment).permit(:comment, :book_id, :user_id)
  end

/bookers2-debug/app/controllers/books_controller.rb

 def show
      @book = Book.find(params[:id])
      @user=@book.user
      @new_book=Book.new
      
      @book_comment = BookComment.new
      @book_comment.user=current_user
     
      @book_comments = @book.book_comments.all
  end