Sign editing screen can no longer be retextured

The bug

It is no longer possible to change the texture used in the background while editing signs.

Previously, the sign editing screen copied the texture used in game menus (MC-269077), which was incorrect as the sign editing screen is not a menu. However, the fix for this appears to have taken away the ability to give this screen a customizable background altogether.

How to reproduce

A resource pack is attached to this issue which retextures the UI background in 24w09a/24w10a versus the latest version.

Expected results

Changing the texture of the sign editing background would still be possible like it was previously.

Actual results

It is now completely impossible.

How to fix

A new texture file should be introduced for the sign editing background, which is distinct from the "menu background" file.