Apply accepted review polish: functional setState, safer probe script, let-bound probe, drop trace

Four style items accepted from the PR #3953 second-round triage:

- Starter counter (dummy JSX + docs snippet) uses the functional update
  form setCount((c) => c + 1).
- The console-log probe message is passed to execute_script as a
  Capybara argument instead of interpolating Ruby into the JS string.
- The probe message local is promoted to let(:log_probe_message).
- The starter view drops trace: true (raise_on_prerender_error stays).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

Author: justin808

docs/oss/building-features/client-side-routing-instant-navigation.md

@@ -84,7 +84,7 @@ const ShellLayout = () => {
       <nav>
         <Link to="/dashboard">Home</Link>
         <Link to="/dashboard/reports">Reports</Link>
-        <button type="button" onClick={() => setCount(count + 1)}>
+        <button type="button" onClick={() => setCount((c) => c + 1)}>
           Clicks: {count} {/* survives navigation — the shell never unmounts */}
         </button>
       </nav>

react_on_rails_pro/spec/dummy/app/views/tanstack_starter/index.html.erb

@@ -18,5 +18,5 @@ https://github.com/shakacode/react_on_rails/blob/main/REACT-ON-RAILS-PRO-LICENSE
     Turbo-coexistence track. -%>
 <div data-turbo="false">
   <%= react_component("TanStackStarterApp", props: @starter_props, prerender: true,
-                      raise_on_prerender_error: true, trace: true) %>
+                      raise_on_prerender_error: true) %>
 </div>

react_on_rails_pro/spec/dummy/client/app/ror-auto-load-components/TanStackStarterApp.jsx

@@ -57,7 +57,7 @@ const ShellLayout = () => {
   return (
     <div className="container">
       <h1 id="tanstack-starter-shell">TanStack Router Starter</h1>
-      <button id="tanstack-starter-counter" type="button" onClick={() => setCount(count + 1)}>
+      <button id="tanstack-starter-counter" type="button" onClick={() => setCount((c) => c + 1)}>
         Shell counter: {count}
       </button>
       <nav>

react_on_rails_pro/spec/dummy/spec/system/tanstack_starter_spec.rb

@@ -100,7 +100,7 @@
     # goog:loggingPrefs browser=ALL option set on rails_helper's
     # *_with_logging drivers). Without this probe, a broken log channel would
     # return [] and the hydration-error assertion would pass vacuously.
-    log_probe_message = "tanstack-starter-console-log-probe"
+    let(:log_probe_message) { "tanstack-starter-console-log-probe" }
 
     before do
       # Drain console entries left over from earlier examples in the shared
@@ -117,7 +117,7 @@
       expect(page).to have_css("section#tanstack-starter-server-data")
       expect(page).to have_text("Server data from Rails RSC payload endpoint")
 
-      page.execute_script("console.error('#{log_probe_message}')")
+      page.execute_script("console.error(arguments[0])", log_probe_message)
       console_entries = page.driver.browser.logs.get(:browser)
       expect(console_entries.map(&:message)).to include(a_string_including(log_probe_message)),
                                                 "Browser console log channel is unavailable; cannot assert " \