Open Pets using the paw icon on the left. The two counters at the top track different things:
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Paw counter — equipped pets. In the inventory pictured here, 1/3 means one pet is equipped out of three available slots.
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Bag counter — owned pets. 3/100 means three pets occupy an inventory with room for 100 in this example.
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Green checkmark — equipped status. The first Dog has a checkmark; the second Dog and Frost Angel are owned but not equipped.
Read your own counters for your current limits. Simply having a pet in the inventory does not mean it is equipped.
At the bottom, Equip Best is the automatic selection option, and Unequip ALL is the option for clearing your equipped selection.
AddPetEquip is a separate game-pass listing. Find it in the game pass directory.