I tried using Reflection the set the "C" ("bedWorks" in Mojang mappings) field and the "D" ("respawnAnchorWorks" in Mojang mappings) field of the DimensionManager of my World. Respawn anchor worked as intended but beds didn't change. So I asked for help on the Spigot forums and no real fix to the problem. After that I tried using the Spigot source to find the issue. I found that the bed explosion check was moved to EntityPlayer by CraftBukkit. And it checks for DimensionManager#isNatural(). I checked for usages of this method and it's also used for Piglin spawning at portals in the overworld.

TL;DR: Bed explosion checks for DimensionManager#isNatural() instead of DimensionManager#isBedWorks() in EntityPlayer#getBedResult(BlockPosition, EnumDirection)