Good question,
a cat, despite its domestication, is a wild animal that retains its hunting instincts. You can see this when playing with cats and witnessing that a cat demands play even multiple times a day to use their built-up energy. Having a cat at home constantly is therefore not fully aligned with their nature. Some would say that they can easily get used to a home environment and they would be right, however if the cat was used to going outside and their owners relocated, it could make your little predator very unhappy.
A good question then would be, despite their nature, why do cats tend to visit the homes of people, sometimes even wanting to stay and often coming back? Isn’t that a sign that cats are happy at home? I think that cats look for a resourceful and safe environment (free food from humans, a perfect cat bed / house, clean towels to sit on etc.). Cats understand that you could be a very valuable resource.
It’s getting confusing, so are indoor cats happy or unhappy?
I would say that the final verdict is that cats are most happy when they can leverage your resourceful household, having their territory secured, while also being able to go outside anytime they want. If this is your situation and you take good care of your cat, then they are most probably happy. If you are not able to provide an outdoor environment, you can easily recognise when your cat is unhappy. A very strong sign that your cat is unhappy is when they go to the toilet in the wrong / an unusual place. Alternatively, signs of happiness and even of ‘cat love’ would be when a cat watches you with narrow eyes, when they expose their sensitive body parts to you without having fear (if you can touch or even cuddle them on their tummy, they really trust you) or when they say “hi” to you when you return from outside. A strong love signal is when they touch their little wet nose gently to your nose (without trying to clean themselves).
So yes, house cats can be very happy after all,
it is however a complex question touching more aspects of a cat’s life from their history to how much they like the humans in the household. They can also have good and bad moods without being strictly unhappy while living with you. It is a little similar to humans. Are you always happy being at home?
I hope you are indeed happy, even if you probably just thought about many things that could be improved in your life. Perhaps cats think in exactly the same way…