PSA: If you are having trouble with your pals leaving their breeding pens
... check that the breeding ranch is fully within your base's blue circle.
The building is massive, and the game lets you have part of it outside, but I ran into a ton of bugs with pals going into a weird state where they can't be assigned after they un-assign themselves to the pen (usually when fast travelling).
Pals need to not be hungry or stressed to be assigned.
Put a food basket inside the pen to keep them from leaving to eat and getting distracted. Don't use raw/cooked berries in general, they don't provide enough food to meet the need within the 3 item per feeding limit. If you only use berries, their time spent working(e.g. breeding) will be shortened before having to go eat again. It is best to manually feed them to full if they are not full already.
Try to keep any other job stations away from the breeding pen to avoid distractions.
Don't both trying to block the entrance, they will just glitch out of the enclosure.
You can have some of the back outside the base circle, I would keep the backside of the hay inside the circle.
Pretty much anything else cooked is better. I am lazy and don't bother with cows, chickens, or bees normally; so I use jam filled buns and salads. Jam filled buns are over twice as nutritious with 6x sanity compared to cooked berries, salads are 4x/11x.
Jam filled buns are probably the best low effort and high yield staple food. You need both berries and wheat for cakes and it doesn't eat into your honey, eggs, or milk. Salads are great if you can invest the pal workload and space into them, but it is sustainable to farm up jam filled buns on one base with minimal dedicated workload and supply 3 full bases.
I usually keep the breeding feed box stocked with salads and the rest have jam filled buns. I do manually feed the breeders to keep them up while I go off and adventure but otherwise they are fine.