How do I fix this?

did you find a fix by chance? i have the same issue but mine is also missing the 3d texture

They responded to my comments on Curseforge but I can't find the resource pack yet.

I have this same issue too. Minecraft v1.21.1 on fabric.
Disabling enhanced beds from Enhanced Block Entities solved the issue.

The issue here, i think, is that the texture for the bed is rotated 180º.

We can see here in the screenshot that the block placement itself is correct, but the texture is not matching the block placement.

Still an issue as of version 1.20.1, i also have "Enhanced beds" from Enhanced Block Entitites disabled.