We are talking on different levels. The discussion here is very high levels of attainments, which is the death of an arahant, then there’s no more rebirth, therefore no more arising of the 5 aggregates, which includes no feelings.
The “no feelings” used by common usage of psychology which I suspect you’re using in this way, is actually not no feelings within Buddhism. It’s numbing of feelings, usually, feelings of unpleasant nature, of which the person numbs, suppresses it, as a wrong method to be “good”, “calm” etc.
It’s one of the common pitfalls along the path of training, of misunderstanding how to deal with feelings, how to practise equanimity. Equanimity is feeling feelings, but not being affected by them, not reacting with likes or dislikes, greed or hate. One should be mindful of feelings.
As long as one is in samsara, unless for the absorption meditation of cessation of perception and feelings, there are feelings. Pleasant, unpleasant or neither pleasant not unpleasant. These feelings are before emotions and do not include emotions. Emotion is classified under volitional formations.
For one who numbs feelings, it’s not that they don’t have feelings anymore, it’s that they ignore, or using aversion to suppress the feelings.
The only way to have truly no feelings is cessation.
Yes, there’s happiness in samsara, or else beings would not be attached to samsara. The problem is as always, it’s impermanent. What’s impermanent is unsatisfactory. Including the happiness of samsara. Only the happiness of (pari)nibbana is permanent, for having no more feelings to change.
For the arahants who are still alive, they too have feelings, and their emotions are basically the brahma viharas, loving kindness, compassion, altruistic joy and equanimity, without any defilements of greed, hated or delusion.
Part of the training is indeed to go beyond being, being/becoming/existance (bhava) is one of the chains of dependent origination, which upon dependent cessation ceases too. Including being human. So being human is something to be overcome upon enlightenment. This is high-level teaching, for those who are not yet even humans (animal-like morality behaviour), they first should be taught to be human first (5 precepts morality).