Death screen background cannot be retextured

The bug

The red, translucent background on the death screen cannot be changed via resource packs. This is in contrast to all other non-in-game menu screens, for which this is possible as of 24w09a.

How to reproduce

1. Download and apply the attached resource pack
2. Die
3. Click "Title Screen"
4. Compare the backgrounds

Expected results

Both would use the "BG" texture.

Actual results

Only the confirmation menu shows this texture.

How to fix

Ideally, the death screen should be given its own texture file instead of copying from the existing menu background, let's call it "death_menu_background.png"?