Clean up model picker input styles

[daviddossett]

Cleans up leftover model picker input styles after the focus outline removal:

• Remove background color from the filter input (was left behind when focus outlines were removed)
• Add spacing below the filter separator to match the gap between the last model item and the "Other models" separator section

[Copilot]

Pull request overview

Adjusts the Chat model picker dropdown’s filter input styling to better match the action widget’s visual design after prior focus-outline changes.

Changes:

• Makes the model picker filter input background transparent.
• Adds extra spacing below the filter area by applying a margin to its container.
• Adds a runtime class to the filter container to target the new spacing rule.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

File	Description
src/vs/workbench/contrib/chat/browser/widget/media/chat.css	Removes filter input background and adds container margin styling for spacing.
src/vs/workbench/contrib/chat/browser/widget/input/chatModelPicker.ts	Adds a CSS class to the filter container at runtime to enable the new spacing rule.