Zombies do not make any effort to break wooden doors, even if they are in the way of a villager or the player. There is no sound, and no cracking animation. This was checked on every difficulty, including Hard.
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Don't be so hasty- I placed it facing out, like regular Villager houses. I'll attach another picture highlighting placement.
Oops, this is a bit embarrassing- I had /gamerule mobGriefing = false on that world. Thanks for checking anyway.
You placed the door the wrong way and opened it. Zombies and villagers cannot destroy/open these doors.