fix(nav): close the site menu when search opens

[simonhamp]

The Search button lives inside the site menu. The menu is a popover, and browsers draw popovers above everything else on the page. DocSearch adds its modal to the page body, so opening search from the menu left the menu sitting on top of the search box. This happened on desktop and mobile.

Now the menu closes when search opens:

• Clicking Search sets showMobileMenu = false in the same click handler, like the theme buttons already do. The menu is gone before the search modal's first frame.
• Cmd+K and / open search without touching the button, so DocSearch's onOpen callback now fires a docsearch:open window event and the menu listens for it.

Things to watch for:

• With Cmd+K the menu can still show for a frame or two, because DocSearch calls onOpen after it paints.
• After closing search that was opened from the menu, focus lands on the page body instead of the Search button, since that button is inside the closed menu. Cmd+K with the menu closed already behaved this way.

I tested it in headless Chrome at 1440x900 and 390x844 on the home page and a scrolled docs page, clicking Search and pressing Cmd+K with the menu open. Scroll behaviour is unchanged. NavigationMobileMenuSearchTest covers both halves of the wiring and fails without the fix.

🤖 Generated with Claude Code

[coderabbitai]

Important

Review skipped

Auto reviews are disabled on this repository. Please check the settings in the CodeRabbit UI or the .coderabbit.yaml file in this repository. To trigger a single review, invoke the @coderabbitai review command.

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Advanced

Run ID: 56c87fc7-f0c5-4071-ae18-b92780eb6fb3

You can disable this status message by setting the reviews.review_status to false in the CodeRabbit configuration file.

Use the checkbox below for a quick retry:

• 🔍 Trigger review

---

_{Comment @coderabbitai help to get the list of available commands.}