fix(core): keep the header search input in document flow

[pringelmann]

• Resolves: Remove absolute positioning from the header search input #61650

Summary

The unified search trigger was absolutely positioned to center it in the header, which placed it after the right-hand items in the DOM. Tab order no longer matched the visual order (the app-injected Assistant button tabbed before search)

This moves the #unified-search mount into a dedicated header-center zone and centers it with symmetric flexbox, instead of absolute positioning. The centering is scoped so behaviour elsewhere is unchanged.

Checklist

• Code is properly formatted
• Sign-off message is added to all commits
• Tests (unit, integration, api and/or acceptance) are included
• Screenshots before/after for front-end changes
• Documentation (manuals or wiki) has been updated or is not required
• Backports requested where applicable (ex: critical bugfixes)
• Labels added where applicable (ex: bug/enhancement, 3. to review, feature component)
• Milestone added for target branch/version (ex: 32.x for stable32)

AI (if applicable)

• The content of this PR was partly or fully generated using AI

[susnux]

That breaks tab order (DOM position no longer matches visual position)

Well I think the problem is that the assistant is not mounting it self correctly.

[pringelmann]

That breaks tab order (DOM position no longer matches visual position)

Well I think the problem is that the assistant is not mounting it self correctly.

Yes that too :) but either way the absolute positioning creates problems for the elements around it

[susnux]

but either way the absolute positioning creates problems for the elements around it

Sure!

But how do you properly center the element when left and right have different sizes?
As it should be absolutely centered, no?

What if size > 512px but appname is very long?

[pringelmann]

but either way the absolute positioning creates problems for the elements around it

Sure!

But how do you properly center the element when left and right have different sizes? As it should be absolutely centered, no?

What if size > 512px but appname is very long?

Both side areas are flex: 1 0, so they're always equal width regardless of content, which keeps the search on the true midline, not just centered in the leftover space. So it is absolutely centered.

A long appname doesn't shift it either. And now that the input is in flow, the label can ellipsize at the header-start edge instead of running under the search:

resize.mp4

That truncation is a small follow-up, but it's only possible because we dropped the absolute positioning.

[pringelmann]

/compile rebase