Search Bar Custom Position

I have seen couple of issues from the past to have searchPlaceholder. Is there a way to have the search bar positioned next to the action buttons? If this feature already exists, please point me in the right direction. I couldn't find a proper solution.

## Expected Behavior
To be able to change the position of the search bar right next to the search button/icon

## Current Behavior
The search bar opens to the left of the toolbar while the button is on the right

No files, tests, or entry points are named. Start by tracing the toolbar's search-bar and action-button rendering, then check existing positioning options and related issues. Done means the search bar can be configured to appear next to the action button, with the existing layout preserved by default.

Written by the indexing model from the issue text.