Add a search field on model selector / improve mobile display (#17765)

Add a search field on model selector / improve mobile display (#17765)

* webui: add search field to model selector and fixes mobile viewport overflow

* webui: simplify model search style and code

* refacor: Search Input component & consistent UI for Models Selector search

* feat: Use Popover component + improve interactions

* fix: Fetching props for only loaded models in ROUTER mode

* webui: prevent models selector popover from overflowing viewport

Use Floating UI's auto-positioning with 50dvh height limit and proper
collision detection instead of forcing top positioning. Fixes overflow
on desktop and mobile keyboard issues

* webui: keep search field near trigger in models selector

Place search at the 'near end' (closest to trigger) by swapping layout
with CSS flexbox order based on popover direction. Prevents input from
moving during typing as list shrinks

* chore: update webui build output

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Co-authored-by: Aleksander Grygier <redacted>