Google isn't exactly helpful. I tried searching for Minecraft Xbox 360 version conversion door bugs, but the most helpful thing I got was a Gemini answer, and after a while, I was like "what on God's green Earth are you babbling about?"
The world (and, I think, this particular structure) was from my Xbox 360 Edition world. It got converted to Xbox One. Then it got converted to Bedrock version. As far as I can recall it's an old bug. Hence the exhibit space.
This screenshot is from current Windows Bedrock version. Previously in this world, the block was (as I recall) a grass-topped dirt block with "upd ate" [sic] written on it in green pixel text. I was actually surprised today when I loaded up this world and saw that it now has a completely new question mark texture! When I converted the world to Java format in Chunker a few days ago, the block was (predictably enough) completely gone. (Don't have the error log at hand sorry)
So which exact conversion bug was this? What exact version of Minecraft had weird door conversions? I'm sure this is documented somewhere!
As you can see from the screenshot I try to keep the world generation bugs and weirdnesses as an exhibit, but, well, I guess the time ran out on this one.
Good question. I recall myself using the force field trick in 2013-14 so back then it was possible to place half doors in editors and the game kept them. But that hardly narrows it down.