Update style of top bar search and fix a11y concern

What does this MR do and why?

• Align to the right
• Move to the right of temporary items like "New look" widget
• Fix accessibility concerns at narrower viewport widths

References

• Feedback : Search bar back in the top nav (#527592)
• ✂️ UX Paper Cuts 17.11 → Verify (#512693 - closed)

Screenshots or screen recordings

Viewport size	Before	After
xs (<576px)
sm (>=576px)
md (>=768px)
lg (>=992px)
xl (>=1200px)

Focus state for icon-only button:

Before	After

How to set up and validate locally

1. Check out this branch
2. Visit the GDK
3. If necessary, turn on the :search_button_top_right feature flag
4. If necessary to get the Duo chat button to appear in your GDK (purely for spacing purposes, there is no functional change to it), apply this patch:

diff --git a/ee/app/views/layouts/nav/_ask_duo_button.html.haml b/ee/app/views/layouts/nav/_ask_duo_button.html.haml
index a759dbdafa64..2a3271f79066 100644
--- a/ee/app/views/layouts/nav/_ask_duo_button.html.haml
+++ b/ee/app/views/layouts/nav/_ask_duo_button.html.haml
@@ -1,4 +1,4 @@
-- if ::Gitlab::Llm::TanukiBot.show_breadcrumbs_entry_point?(user: current_user, container: @group || @project)
+- if ::Gitlab::Llm::TanukiBot.show_breadcrumbs_entry_point?(user: current_user, container: @group || @project) || true
   - label = s_('DuoChat|GitLab Duo Chat')
   - chat_disabled_reason = ::Gitlab::Llm::TanukiBot.chat_disabled_reason(user: current_user, container: @group || @project).to_s

MR acceptance checklist

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