Web SearchField clear button is not centred and the search icon differs between designer and browser

The Web SearchField's clear button is not vertically centred in the field and sits too far from the right-hand edge, wasting horizontal space in both the visual designer and the running app. The field also shows no search icon in browsers, while the visual designer draws a small, unclear magnifier character, so the two appearances do not match.

Expected: the clear button is vertically centred and close to the field's right edge, and the search field shows the same clear magnifier icon from the system-symbol catalogue in the designer and in every browser.