There used to be a lot of cats in my village,At that time, there was a bug that the game would slow down when the villagers are working. I think it was the problem of the cats because after killing them, the game would return to normal until the cats appear again. But cats no longer appeared after upgrading the game.And iron golems never appeared in this village.Please look at the pictures I sent.
Picture 1:Here is my village and there are no cats or iron golems.
Picture 2:I used the instruction to kill all the villagers,It's strange that the cats appeared after that.
Picture 3:I created many villagers.
Picture 4:The next day, when the villagers start to work, an iron golem finally appeared
We are unable to reproduce iron golems not spawning when conditions are met.
According to the 1.16.0.51 changelog, the new rules for iron golem spawning include the following:
From your description, it sounds like iron golems began to spawn as soon as this condition was met.
Regarding the cats, it is possible that the village still exists in the game's memory and that individual villagers are not removed from its registry for a period of time after they are killed. In this situation, cats will still spawn based on the number of beds that exist within the village boundaries. That would explain Picture 2. As for picture 1, you have not said how much time you waited for cats to spawn, so I am unable to evaluate your report that cats were not spawning when conditions were met.