Regardless of which block state property is set, and even when set to the wall variant of hanging signs, block displays of hanging signs always seem to render as the attached variant.

To reproduce:

1. Run commands:

   /summon block_display ~ ~ ~ {block_state:{Name:"minecraft:acacia_hanging_sign",Properties:{attached:"false"}}}

   /summon block_display ~ ~ ~ {block_state:{Name:"minecraft:acacia_hanging_sign",Properties:{attached:"true"}}}

   /summon block_display ~ ~ ~ {block_state:{Name:"minecraft:acacia_wall_hanging_sign"}}

2. Note that all three entities display the same block state.