Regarding the 3 types of suffering as above, usually the way I explain this to beginners are as follows. Do comment on your understanding and if my understanding is in accordance to the Dhamma.
Suffering suffering: the normal unpleasant mental feelings, and all forms of physical sufferings. Including depression, mental illness, death etc. Arahants have no more mental sufferings, but they can have physical sufferings in this category. (I am still unsure if arahants can have unpleasant feelings of the mind.)
Suffering due to change/ perishing. In the sense that even pleasant feelings are suffering purely because it’s impermanent. Playing video games, being a billionaire, financial freedom, life in heaven is also can be classified as under this. Any attachments to anything impermanent is under this suffering. Arahants do not have this suffering.
Suffering due to conditioning. This is the deeper sense of suffering. Say as a lay person, one is forced to work. If don’t work, no money, hunger is the suffering suffering experienced. If work, then even when it’s going good, can have time to play video games, there’s also suffering due to change. If one is tired of all these and wishes to immediately get out of this conditioned existence, one cannot immediately do so, but has to develop the full noble 8fold path, including the tired of all samsara factor. So the conditionings of the world is such that we have to play by the law of cause and effect, kamma, etc, not by our own wishes. This is the inherent suffering of conditioning. Even Arahants have to eat, go to toilet etc, so they too have to experience this kind of suffering as long as they had not pass their final death. They have an advantage of being able to go deep into absorptions to suspend their existence here for a while before having to get out of there and eat again.
Am I accurate? Especially with regards to arahants.