Easy to reproduce: put down a bunch of iron doors and break them with your bare hands. If you break the top half of the door, the lower half will drop. If you break the bottom half, nothing will drop.
Noticed this because I was playing around with custom loot tables for doors and beds–it looks like the issue is that the half that breaks automatically doesn't take into account the tool the player used to break the first half, so it drops even if the player's using a tool that shouldn't be able to drop that block.
This bug seems to also apply to beds, tall flowers, and tall grass and ferns, but isn't noticeable there because they don't normally care what the player uses to break them.
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Can confirm in 20w46a.
Can confirm in 21w03a.

This issue prevents MC-4378 to be fully fixed.

This might be caused by the fix of [MC-136085] if this wasn't an issue in 1.15.2

Can confirm for 1.16.5

Can confirm in 1.17.1.

Confirmed for 22w44a
Cannot reproduce in 1.21-pre2. Breaking the top half of an iron door with my bare fist didn't drop the door.
Also cannot reproduce, except in 1.21-pre4.
Edit: Was fixed in 1.20.3-pre3 along with MC-266115.
Confirmed, as mentioned, easiest way to reproduce is to break iron doors with your bare heands.