Hide 'Ask Gemini' text box in embed layout

[parlough]

As it's distracting in embedded versions of DartPad, which are often focused codelabs or tutorials. This change keeps gemini fixes for analysis errors though, only hiding the text box.

[github-actions]

PR Health

Breaking changes ✔️

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API leaks ✔️

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License Headers ✔️

// Copyright (c) 2025, the Dart project authors. Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.

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Unrelated files missing license headers

Files
pkgs/samples/lib/brick_breaker.dart
pkgs/samples/lib/fibonacci.dart
pkgs/samples/lib/hello_world.dart
pkgs/samples/lib/main.dart
pkgs/samples/lib/sunflower.dart