Add Kapa AI to the search widget

[juliusv]

This is a fourth alternative to the three explorations by @ArthurSens that all add a new top menu item:

• Kapa AI in a sidebar drawer: website: add a drawer-based Kapa Ask AI prototype #2958
• Kapa AI in its own modal: website: add a modal Kapa Ask AI prototype #2959
• Kapa AI on a separate page: website: add a page-focused Kapa Ask AI prototype #2960

I think I like the modal variant, but I would like to avoid adding a whole new top menu item (we should be using that space very sparingly). This fourth alternative integrates the AI search into the existing Search / Spotlight experience, by adding an "Ask AI" button after you open the search (and changing the header field placeholder to "Search / Ask AI").

This is similar to how it's done on grafana.com.