Furnace GUI is sometimes displayed incorrectly after relogging

The bug

If you replace the fuel in a lit furnace with a worse fuel, then the furnace GUI will appear glitched after relogging. This has always been the case (see MC-10025); however, the glitch is far more severe as of 23w31a.

How to reproduce

1. Put raw beef in the ingredient slot of a furnace
2. Put a piece of coal in the fuel slot
   → The coal is consumed
3. Put a stick in the fuel slot
4. Close and reopen the world
5. Open the furnace GUI
   → The furnace GUI appears glitched