Golems and cats are not spawning naturally in a village with over 30+ villagers.  The village has 65 beds, many houses with valid doors, and villagers are regularly fed (albeit manually).  There are zero new golems since the update after the population grew, with the same going for cats.

Accroding to Minecraft gamepedia: "In order for a village to spawn iron golems, 75% of the villagers in the village must have worked in the past day, and 100% of the villagers must be linked to a bed. The chance of spawning is ¹⁄₇₀₀ per game tick, which averages to one every 35 seconds."