What is the reason for declaring someone an unbeliever (kafir) if they say that whoever affirms prayer, zakat, fasting, and Hajj is a believer, as long as they are not denying it in their heart?

The disbelief mentioned in the narration relates to the Jahmiyyah's error in defining faith as mere knowledge, affirmation, or acknowledgment. This is a generic disbelief, not specific to an individual. Imam Ahmad differentiated between the Murji'ah and the Jahmiyyah. Imam Ahmad and the Salaf imams did not generally declare the Murji'ah to be disbelievers, but they declared the Jahmiyyah to be disbelievers because of their saying that faith is only affirmation or knowledge, which the Salaf denounced. Wakee' ibn al-Jarrah and Ahmad ibn Hanbal strongly condemned this statement and considered it disbelief because it would imply that Pharaoh, Iblis, and Abu Talib were believers. However, the declaration of disbelief here is for the type, not for the individual. Not everyone who holds the view of the Jahmiyyah is judged to be an individual disbeliever; rather, disbelief is a judgment on the statement itself. A specific person is not declared a disbeliever until the legal proof is established against them.