Make command palette node more prominent in the center of the admin bar

[fushar]

We want to update the design of the command palette node in the admin bar, by making it more prominent in the center.

This is a continuation of https://core.trac.wordpress.org/ticket/64672, where we decided to make it a simple icon node at that time.

Trac ticket: https://core.trac.wordpress.org/ticket/65219

This PR is an attempt to take ​https://github.com/WordPress/wordpress-develop/pull/11171 to the finish line. On top of that PR, I improved mobile styles, background colors, and command palette overlay behavior.

Basically, we want to make the command palette "trigger node" more prominent in the center of the admin bar. On mobile viewport, to make the layout balanced, I propose to put the icon at top-right, together with the user avatar icon.

Desktop	Mobile

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The trigger node is not an actual text input form. So, I made the following improvements:

• Change color on hover to make it look like a button.
• Move the command palette overlay to the top, to cover the node. This behavior is similar to Slack. (I was inspired by this comment ​https://github.com/WordPress/wordpress-develop/pull/11171#pullrequestreview-3917555903)

​https://github.com/user-attachments/assets/229fd39f-e98e-45c7-83ab-3381f630a7fc

I used the following color variables, which is a bit different from the original PR. I believe the new color is more subtle and look better. It looks more like button than text input now.

Normal	Hover

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Here's how it looks like on all color schemes:

Normal	Hover

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The trigger node is responsive; it can reposition and resize itself in a crowded admin bar:

​https://github.com/user-attachments/assets/c8120b13-9a05-4127-ab1c-c5527c337aea

## Use of AI Tools

AI assistance: Yes
Tool(s): Claude Code
Model(s): Claude Opus 4.7
Used for: CSS implementation under my supervision.

[westonruter]

This has been previously discussed, in part:

• ​https://github.com/WordPress/wordpress-develop/pull/11171#pullrequestreview-3917555903
• ​https://github.com/WordPress/wordpress-develop/pull/11171#issuecomment-4003269084
• ​https://github.com/WordPress/wordpress-develop/pull/11171#pullrequestreview-3894717813

Plugins very often add admin bar menu items, which puts real estate in the admin bar at a premium. This is especially so on smaller screen sizes, and extremely so for mobile. There would be no room for such a faux command palette search bar on mobile (although you are accounting for in ​your PR). To me there seems to be very little value to have a wide command palette bar taking up room in the admin bar which only serves the purpose as being a very large button which opens the actual command palette in a modal with its own input field. With the keyboard shortcut appearing in the admin bar, the intention is for users to use the keyboard to invoke the command palette anyway, and not to click the admin bar anyway.

[joedolson]

I agree with @westonruter; the command palette is intended to be a mechanism that intentionally occupies a minimal surface in the UI, offering a quick access via keyboard. Giving it a large UI priority in a heavily used area doesn't seem helpful.

[wildworks]

I agree with @westonruter, too. This ticket might be closed as "maybelater".