Move command palette to the right and make it more visible

[fernandot]

The command palette has great potential not only for quick access but also for future chatbot-style interactions with AI connectors. For these reasons, I believe that its current location and appearance do not support its intended use, so I propose two changes:

1. Move it to the right of the admin bar, next to the user profile link, where it will be much more visible, since on the left side it will always compete with a multitude of other links and elements that make it invisible
2. Make the text input box visible directly on the admin bar, while maintaining the current Ctrl/Cmd+K functionality, to make it more

[sabernhardt]

Related: #64672

[audrasjb]

Removing trunk version as this is not going to be shipped with WP 7.0 but in the next releases.

[desrosj]

Since this is an enhancement, there's no first version of WordPress this can be reproduced in. Removing trunk version.