The outcome has been further verified by testing in a single-player world, and behaviour still remains. The suggestion is appreciated, Dhranios!
This bug is accurately covered and encapsulated by: MC-157385
I was unable to initially find this report, though I blame this on my inaccurate use of keywords in my search, and the lack of thoroughness in my search. Thank you Jiingy for notifying me.
Upon further testing, it appears that the cats become stuck once a villager enters the house, opening the door and clearing the pathway to the bed momentarily, before closing the path again and locking the cats into trying to get to an inaccessible bed.
I have started experiencing this bug in the most recent version, 1.20.4. I'd initially made my own bug report, not knowing this one was already opened, and I also include two separate videos of the event transpiring, though both are without the debug screen enabled. I have just retested the bug once again, with debug screen active, and the file is now attached as "Minecraft Cat Bug Report Final.mp4".