Protip for maximizing Cat Companion bond leveling and not making the same mistakes I did. There are two types of Bond level - The cat's own bond (Red circle) and Cat/Goose Group bond (Green circle). The group bond is a sum of all bond levels of the particular pet type and that's where most of the better rewards are like pet carrying idle pose, pet carrying function etc.
The cat bond goes up to 10k points, and the group bond caps at 30k. You have a slow regenerating stamina system to perform activities that grant 300 bond points to all cats or 150 to all cats+geese so it's better to spread out the bond level of the cats evenly because if one cat is already at max bond, they stop gaining bond exp that contributes to the group bond level.
With the same logic, it's more worthwhile to do the group stamina activity the more cats you own. You can recruit 1 pet a week by buying the ticket from the shop. If Global follows CN, they might mail you 10 pet stamina refills for the group activity. I recommend only using them when you have recruited at least 3 cats to maximize the group bond gain (the fourth cat is still unavailable)
You also get 300 interaction stamina daily to pet your cats. Just pick a favorite pet and pet them (for cats) or duel them (for geese) to raise bond.
The pet MVP costs 20k currency to exchange, and 10k each for the scenario and idle poses. Idle pose requires max group bond, so I recommend not splurging them on the cat outfits yet and just save them. I'm almost 2 months and have just hit 20k coins.