FIX: correctly handles mobile and default (#23152)

This commit ensures we have correct icon and title on mobile for the chat header icon.

It also fixes a bug where the site setting was not correctly used when the user has not yet set the user option.

Both cases are now correctly tested.

plugins/chat/spec/system/separate_sidebar_mode_spec.rb

@@ -17,6 +17,36 @@ RSpec.describe "Separate sidebar mode", type: :system do
     sign_in(current_user)
   end
 
+  describe "when separate sidebar mode is not set" do
+    before do
+      SiteSetting.chat_separate_sidebar_mode = "always"
+      chat_page.prefers_full_page
+    end
+
+    it "uses the site setting" do
+      visit("/")
+
+      expect(sidebar_component).to have_switch_button("chat")
+      expect(header_component).to have_open_chat_button
+      expect(sidebar_component).to have_no_section("chat-channels")
+      expect(sidebar_component).to have_section("Categories")
+
+      chat_page.open_from_header
+
+      expect(sidebar_component).to have_switch_button("main")
+      expect(header_component).to have_open_forum_button
+      expect(sidebar_component).to have_section("chat-channels")
+      expect(sidebar_component).to have_no_section("Categories")
+
+      find("#site-logo").click
+
+      expect(sidebar_component).to have_switch_button("chat")
+      expect(header_component).to have_open_chat_button
+      expect(sidebar_component).to have_no_section("chat-channels")
+      expect(sidebar_component).to have_section("Categories")
+    end
+  end
+
   describe "when separate sidebar mode is never" do
     before do
       current_user.user_option.update!(